Class 10 Maths | Chapter 1 Complex Numbers | Exercise 1.1 Q1 & Q2 | APSACS FIBSE
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[{'start': '1.280', 'end': '5.560', 'text': 'Assalam o Alaikum Dear Students Welcome back to our'}, {'start': '5.560', 'end': '10.719', 'text': 'channel Today our topic is Chapter Number First of 10th Class and its'}, {'start': '10.719', 'end': '16.160', 'text': 'name is Complex Number. To know Complex Number,'}, {'start': '16.160', 'end': '22.160', 'text': 'first of all we need to know Real Numbers. Already we'}, {'start': '22.160', 'end': '26.560', 'text': 'had already explained in Chapter Number First in Class Ninth, Real Numbers'}, {'start': '26.560', 'end': '33.680', 'text': '. We had discussed all these things, Natural Numbers, Whole Numbers, Integers, Rational Irrational. And real'}, {'start': '33.680', 'end': '38.640', 'text': 'numbers, we have discussed all these there, if you guys want to watch then'}, {'start': '38.640', 'end': '43.760', 'text': 'you guys can watch our previous lecture. Now we have talked about complex numbers, so today let'}, {'start': '43.760', 'end': '51.320', 'text': 'us discuss the complex numbers.'}, {'start': '60.399', 'end': '65.440', 'text': 'The definition of complex number is that we have that the sum'}, {'start': '67.720', 'end': '74.560', 'text': 'of real and imaginary'}, {'start': '80.680', 'end': '84.720', 'text': 'numbers are called'}, {'start': '86.320', 'end': '88.960', 'text': 'complex'}, {'start': '91.400', 'end': '97.840', 'text': 'numbers, that is, in this we will have real part and imaginary part too. Now'}, {'start': '97.840', 'end': '102.240', 'text': 'what will be its general form, we will have the general form of'}, {'start': '105.000', 'end': '110.399', 'text': 'a + biot a which We have that, we have the real'}, {'start': '110.399', 'end': '116.880', 'text': 'part and diot, which we have, we have the imaginary part,'}, {'start': '117.640', 'end': '124.880', 'text': 'now we have the general form of complex number, now'}, {'start': '124.880', 'end': '131.080', 'text': 'here we have a note coming that in the note, we have to note'}, {'start': '131.080', 'end': '134.560', 'text': 'that every'}, {'start': '136.520', 'end': '141.640', 'text': 'number is a complex number,'}, {'start': '147.520', 'end': '153.840', 'text': 'now what we have, we have real numbers, which we have, integers, whole numbers,'}, {'start': '153.840', 'end': '159.280', 'text': 'natural numbers, rational numbers, irrational numbers or all the numbers we have,'}, {'start': '159.280', 'end': '164.000', 'text': 'we have them all. What is that, we have complex numbers, now'}, {'start': '164.000', 'end': '169.840', 'text': 'we have the definition of complex numbers, now if you have, we'}, {'start': '169.840', 'end': '175.519', 'text': 'have pure real numbers, like we have examples, what do we have,'}, {'start': '175.640', 'end': '185.360', 'text': 'we have 3 5 7 12 every real numbers, so'}, {'start': '185.360', 'end': '192.440', 'text': 'what do we call these, we call them pure real and if we have 3iot'}, {'start': '192.440', 'end': '200.319', 'text': '7iot 5iot and so on, these are the numbers that we have, these are the numbers that we have, now'}, {'start': '200.319', 'end': '204.879', 'text': 'this is what we have. We have pure real numbers, it is also called complex number, this'}, {'start': '204.879', 'end': '210.400', 'text': 'is already we have a complex number because here we have three which we have'}, {'start': '210.400', 'end': '217.200', 'text': 'along with this we can write + 0 iota so that we have the general form of complex'}, {'start': '217.200', 'end': '225.680', 'text': 'number, similarly we have 3iot, this is equal to 0 + 3iot so that this'}, {'start': '225.680', 'end': '230.000', 'text': 'becomes the real part of ours and this becomes the imaginary part of ours, then this'}, {'start': '230.000', 'end': '235.360', 'text': 'is also all the pure imaginary numbers that we have or These are pure real numbers, we already'}, {'start': '235.360', 'end': '242.080', 'text': 'have them, these are complex numbers, but in the generalized form, we have a + b iota, so'}, {'start': '242.080', 'end': '247.920', 'text': 'to make a + b iota, we can take +0 iota with this. If these are pure real numbers, then with this we'}, {'start': '247.920', 'end': '253.040', 'text': 'can take +0 iota, that is, the elementary number is present here, but its magnitude'}, {'start': '253.040', 'end': '257.919', 'text': 'is zero with us, so that is why what we have is this, we have a complex'}, {'start': '257.919', 'end': '264.320', 'text': 'number. Now similarly, what we have is pure eminary. There is a number, along with it we can write 0 +'}, {'start': '264.320', 'end': '270.400', 'text': '3iot, so this also becomes the sum of real and imaginary part. Now here'}, {'start': '270.400', 'end': '274.560', 'text': 'in the note, we have written that every number is a complex number, so people'}, {'start': '274.560', 'end': '281.360', 'text': 'can ask you that if we have 7 - 3iot, is this a number,'}, {'start': '281.360', 'end': '287.520', 'text': 'is it a complex number or not? So you guys have to keep in mind that if'}, {'start': '287.520', 'end': '294.000', 'text': 'we have any number, whatever it may be, but we have a number, then it'}, {'start': '294.000', 'end': '300.400', 'text': 'will be complex. Because in the note, we have written that every number is a'}, {'start': '300.400', 'end': '305.759', 'text': "complex number, so that's why it is a complex number, but then if you guys"}, {'start': '305.759', 'end': '311.360', 'text': 'see, here we have written in the definition that the sum of real and imaginary number, so here'}, {'start': '311.360', 'end': '318.080', 'text': 'we have the word sum, then here is subtraction, people'}, {'start': '318.080', 'end': '323.600', 'text': 'can get confused in this, so this is what we have 7 - 3iot, this is what we actually have'}, {'start': '323.600', 'end': '333.360', 'text': ', 7 + -3iot, so this Which is -3iot, we have got the imaginary part and this which'}, {'start': '333.360', 'end': '337.000', 'text': 'we have is seven, this is the real part,'}, {'start': '337.000', 'end': '343.759', 'text': 'so this is the sum of imaginary and real numbers, then again we have that definition also'}, {'start': '343.759', 'end': '349.680', 'text': 'correct with us, so that is why whatever number we have, whether it has iota with it or not'}, {'start': '349.680', 'end': '355.199', 'text': ', all those are complex numbers. Now what is Iota? If someone asks you about Iota,'}, {'start': '355.199', 'end': '361.520', 'text': 'then what is Iota? Whenever any negative sign'}, {'start': '361.520', 'end': '365.919', 'text': 'comes inside the square root, we have this. This is what we have. This image'}, {'start': '365.919', 'end': '372.000', 'text': 'is equal to Iota. As the value of Iota, what we have is Iota = -1 under the root. This'}, {'start': '372.000', 'end': '376.319', 'text': 'is the value of Iota. Now if we take the square root of both the sides, then'}, {'start': '376.319', 'end': '381.360', 'text': 'we will get Iota² and this will become equal to -1,'}, {'start': '381.360', 'end': '387.520', 'text': 'so it means that. What we have is the value of ot² - 1 So here we have'}, {'start': '387.520', 'end': '391.840', 'text': 'something about complex numbers, we have defined and we can share it with you guys.'}, {'start': '391.840', 'end': '396.160', 'text': "Discussed that we have complex numbers, now let's go ahead,"}, {'start': '396.160', 'end': '401.919', 'text': 'we have our chapter number one, complex numbers.'}, {'start': '401.919', 'end': '406.639', 'text': "Let's see in Exercise 1.1, what is asked from us there about the operations of complex numbers, that is,"}, {'start': '406.639', 'end': '411.600', 'text': 'how we will do addition, how we will do subtraction, how we will do multiplication,'}, {'start': '411.600', 'end': '416.560', 'text': 'how we will do division, how we will do division. Now in the exercise, we will know'}, {'start': '416.560', 'end': '420.560', 'text': 'how we have to solve division, how we have to solve subtraction, how we have'}, {'start': '420.560', 'end': '424.479', 'text': 'addition. How to do and how to do multiplication, so let'}, {'start': '424.479', 'end': '430.479', 'text': "'s go to the next exercise. What is asked of us in Exercise 1.1?"}, {'start': '430.479', 'end': '434.960', 'text': 'Now our first question in Exercise 1.1'}, {'start': '434.960', 'end': '441.599', 'text': 'is that we have to simplify and express in terms of yiot, that is, we'}, {'start': '441.599', 'end': '446.479', 'text': 'have to convert it into yiot form. Already we have explained that'}, {'start': '446.479', 'end': '451.360', 'text': 'if we have a minus sign in the bottom root, then it is equal to yiot, so this is what'}, {'start': '451.360', 'end': '459.800', 'text': 'we have. Pass is the first question, it is equal to -3 root, so we can write it as 3 *'}, {'start': '459.800', 'end': '468.720', 'text': '-1 whole square root, now we can write it as 3 * -1 root,'}, {'start': '468.720', 'end': '473.280', 'text': 'so -1 is the value of the under root which we have is equal to iota, so we'}, {'start': '473.280', 'end': '478.160', 'text': 'can write it as 3 and then we will write iota, this'}, {'start': '478.160', 'end': '484.319', 'text': 'will be our answer. Similarly, we have part number second in question number one,'}, {'start': '484.319', 'end': '490.720', 'text': 'we have that 6. - 4 root so'}, {'start': '490.720', 'end': '497.680', 'text': 'we'}, {'start': '497.680', 'end': '503.840', 'text': 'can write'}, {'start': '503.840', 'end': '509.360', 'text': 'this'}, {'start': '509.360', 'end': '513.599', 'text': '.'}, {'start': '513.599', 'end': '520.640', 'text': 'The answer to this'}, {'start': '520.640', 'end': '528.160', 'text': 'will be 12. Similarly, the part number that we have is -4 / 9 whole square root.'}, {'start': '528.160', 'end': '535.800', 'text': 'So we can write that 4 / 9 square root * -1'}, {'start': '535.800', 'end': '542.560', 'text': '-1, this will be the whole square root. Now this is equal to us,'}, {'start': '542.560', 'end': '547.440', 'text': 'we will write the whole square root of two by 3 because the square of two comes to 4 and the square of 3'}, {'start': '547.440', 'end': '552.959', 'text': 'does not come to us and multiply by minus one root, then it will become equal to'}, {'start': '552.959', 'end': '558.640', 'text': 'square and square root. Cancel 2 / 3 and instead of this minus one under the root, we will write'}, {'start': '558.640', 'end': '565.440', 'text': 'ayot, this will give us the answer. Similarly, the fourth part, the sixth'}, {'start': '565.440', 'end': '571.200', 'text': 'part, sorry, the fourth part, this is the fourth part, which is this minus'}, {'start': '571.200', 'end': '581.320', 'text': '* -20 root, so we will write minus in its place, we will write the -20 root as 20'}, {'start': '581.320', 'end': '589.920', 'text': '* -1. Now we can write this as - * 20 [music]'}, {'start': '589.920', 'end': '595.200', 'text': '-1, so this will become equal to us. - Under root of 4'}, {'start': '595.200', 'end': '602.160', 'text': 'and this will become 5 45 20lt by iota, we have minus one under root'}, {'start': '602.160', 'end': '606.399', 'text': 'is equal to iota, so we can take this, we can take it out of the square root,'}, {'start': '606.399', 'end': '615.240', 'text': 'we will have -2 * 5 root and along with this iota, this will come to us, the answer is'}, {'start': '615.240', 'end': '620.959', 'text': 'similarly, we have question part number five, this is equal to'}, {'start': '620.959', 'end': '629.480', 'text': '4 will come in its place, minus this we will have 60 under root * -1'}, {'start': '629.480', 'end': '636.079', 'text': 'root will become 4 - 60.'}, {'start': '636.959', 'end': '643.320', 'text': 'We can also write this like this. Now if you want to simplify further then we can do'}, {'start': '643.320', 'end': '652.560', 'text': '2 * 4 - 2 * 15 15.'}, {'start': '652.560', 'end': '660.800', 'text': 'This will give us the answer. Now we have power on both -8 and -2. We have'}, {'start': '660.800', 'end': '664.880', 'text': 'square root on both of them. So we had already read in the Law of Exponents'}, {'start': '664.880', 'end': '670.720', 'text': 'that if the power is the same then we can common it or if we have the same base'}, {'start': '670.720', 'end': '674.399', 'text': 'then we have the power. The same property will be added if you define it, then we'}, {'start': '674.399', 'end': '682.640', 'text': 'will have equal -8 * -2, power 1/2 is also on this, 1/2 is also'}, {'start': '682.640', 'end': '688.360', 'text': 'on this, so here we can write that -8 * [Music]'}, {'start': '688.360', 'end': '695.200', 'text': '-2 power 1/2, we can write this, multiply -8 and -2, we will get 16 power 1/2'}, {'start': '695.200', 'end': '702.320', 'text': 'and this is equal to 42 power 1/2, these two cancel, so equal to two, we have the answer. This is what'}, {'start': '702.320', 'end': '708.560', 'text': 'we have in question number one, now'}, {'start': '708.560', 'end': '712.640', 'text': 'we have in question number two, here it is written that simplify'}, {'start': '712.640', 'end': '717.279', 'text': 'it, we have to simplify it, we have to make the generalized form form, we have to make'}, {'start': '717.279', 'end': '722.959', 'text': 'the general form of the complex number, so the general form that we have is a + biot, in the same way, we'}, {'start': '722.959', 'end': '728.560', 'text': 'have to convert it into a + biot, so what is the method we have for this, it will come to us'}, {'start': '728.560', 'end': '732.680', 'text': '4-iot, now if we have to eliminate the bracket, then we have'}, {'start': '732.680', 'end': '739.279', 'text': '+5. + 5iot Now we have to write the like term together, then like term, we have these two'}, {'start': '739.279', 'end': '746.600', 'text': 'real parts and these two are imaginary parts, so we will write this as 4 + 5 and -iot +'}, {'start': '746.600', 'end': '754.399', 'text': '5iot, then add 4 and 5, then we have it equal to 9 and if we add 5 -iot, 5iot -iot, then'}, {'start': '754.399', 'end': '761.040', 'text': 'we have it equal to + 4iot, this is how we got the general form,'}, {'start': '761.040', 'end': '766.240', 'text': 'similarly we have the question number. The part number second in two is that we have'}, {'start': '766.240', 'end': '772.399', 'text': 'that 7 - 6iot, I wrote this in its place, now this'}, {'start': '772.399', 'end': '776.240', 'text': 'Here if there is subtraction then in subtraction we have sign change or if you'}, {'start': '776.240', 'end': '779.839', 'text': 'multiply with minus then if we multiply minus with any sign then'}, {'start': '779.839', 'end': '784.480', 'text': 'it changes with us. If there is plus then it will be converted into minus and if there'}, {'start': '784.480', 'end': '788.560', 'text': 'is minus then it will be converted into plus. So this minus here is plus then minus and'}, {'start': '788.560', 'end': '793.959', 'text': 'plus will become -5. If we multiply minus and minus then plus will come. Now we have to'}, {'start': '793.959', 'end': '800.240', 'text': 'do simple plus, so bring the like terms together and write the like'}, {'start': '800.240', 'end': '806.480', 'text': 'terms together, then we will get 7 - 5 - 6iot + 6iota. These two'}, {'start': '806.480', 'end': '811.160', 'text': 'will cancel with each other, so we will get this. From 7 - 5, we will get'}, {'start': '811.160', 'end': '817.519', 'text': '2. If you have to write + 0, then there is no problem,'}, {'start': '817.519', 'end': '822.320', 'text': 'we will get the general form. Now we have which The question is, in question two, part number'}, {'start': '822.320', 'end': '830.639', 'text': 'three is what we have -2 + 8iot - 7 + 3iot. Now we'}, {'start': '830.639', 'end': '835.320', 'text': 'have to multiply this minus again with this and we have to write this in its place -2 +'}, {'start': '835.320', 'end': '839.240', 'text': '8iot [music]'}, {'start': '839.240', 'end': '844.920', 'text': '-7-3iot. If we have to write one term together again, then we will have'}, {'start': '844.920', 'end': '852.320', 'text': '-2 -7 + 8iot -3iot, we will have this -2 and -7'}, {'start': '852.320', 'end': '858.320', 'text': 'we will get -9 and this will get us 8 -3 will come with 5 and along with'}, {'start': '858.320', 'end': '863.560', 'text': 'it iot, we have the general form, we have the general form of complex number,'}, {'start': '863.560', 'end': '871.680', 'text': 'similarly in part number four we have that 4 - 2iot - * 5 - 2iot. Now'}, {'start': '871.680', 'end': '876.440', 'text': 'we have to multiply this minus with this again, then we will get 4'}, {'start': '876.440', 'end': '883.600', 'text': '-2iot. Now if we multiply the minus with this, we will get -5 + 2iot. If we look at like terms'}, {'start': '883.600', 'end': '891.120', 'text': 'together then we will have this 4 -5 and this will become -2iot +2iot These two'}, {'start': '891.120', 'end': '896.199', 'text': 'will cancel again this 4 -5 will become equal to'}, {'start': '896.199', 'end': '902.480', 'text': '-1 We have this we have that we have -1 Answer came this is also a pure real number'}, {'start': '902.480', 'end': '908.240', 'text': "so we have this, we have part number four in question number two Now let's"}, {'start': '908.240', 'end': '913.199', 'text': 'move towards part number fifth in question number two, what do we have in it now Similarly,'}, {'start': '913.199', 'end': '919.519', 'text': 'for the question number two, we have the fifth part, we have that 2 + 4iot * 1'}, {'start': '919.519', 'end': '924.800', 'text': '+ 2iot i.e. how will we multiply two complex numbers, so now we'}, {'start': '924.800', 'end': '929.440', 'text': 'have to multiply the number two by two complex numbers, then we have that we'}, {'start': '929.440', 'end': '933.519', 'text': 'will multiply two'}, {'start': '933.560', 'end': '939.680', 'text': 'with one and then we have to multiply two with 2iot, that is, we have given the real part to the first number,'}, {'start': '939.680', 'end': '943.680', 'text': 'we have given both i.e. real and imaginary part. We have to multiply with both,'}, {'start': '943.680', 'end': '949.040', 'text': 'then we have to multiply the elementary part with both, then we'}, {'start': '949.040', 'end': '956.560', 'text': 'will get 2 * 1 2, plus 2 * 2 = 4iot, now we multiply 4iot with one,'}, {'start': '956.560', 'end': '964.360', 'text': 'then plus 4iot will come and 4 * 2 = 8 iot and iot are multiplied, then'}, {'start': '964.360', 'end': '969.199', 'text': 'we have multiplied it iot². Now we have to simplify it, i.e.'}, {'start': '969.199', 'end': '974.560', 'text': 'the value of iot². And if we have to add the like term, then we will have'}, {'start': '974.560', 'end': '982.399', 'text': '2 + 4iota and if we add 4iot, we will have 8iota + 8. If'}, {'start': '982.399', 'end': '990.120', 'text': 'the value of *ot² is -1, then we will put it -1, then we will have 2 + 8iot -'}, {'start': '990.120', 'end': '997.440', 'text': '8 because plus and minus will come to minus and 8 * 1 = 8, so we will have this 2 - 8'}, {'start': '997.440', 'end': '1005.680', 'text': '+ 8iot This will be equal to -6 + 8iot This is the answer we got i.e.'}, {'start': '1005.680', 'end': '1009.120', 'text': 'how will we multiply two complex numbers, similarly'}, {'start': '1009.120', 'end': '1015.120', 'text': 'multiply the real part with both and then multiply the imaginary part with both, now we have'}, {'start': '1015.120', 'end': '1021.839', 'text': 'part number six, what we have is 1 - 4iot * 2 - 3iot, you can multiply this also in the same way'}, {'start': '1021.839', 'end': '1025.919', 'text': 'or for this we do another method so that you people can understand this.'}, {'start': '1025.919', 'end': '1030.720', 'text': 'Once you understand the method and also the other method, here we have the real part,'}, {'start': '1030.720', 'end': '1036.799', 'text': 'we will write it as one into, we will write this with this, 2-3iot,'}, {'start': '1036.799', 'end': '1043.480', 'text': 'here we have -4iot, we will write this with 2 - 3iot,'}, {'start': '1043.480', 'end': '1047.919', 'text': 'that is, we have seen this with this and we have also seen this with this, now if we'}, {'start': '1047.919', 'end': '1051.280', 'text': 'multiply this, then if I multiply one with this, the same number will come again'}, {'start': '1051.280', 'end': '1054.880', 'text': 'because we have one. Multiplicative identity is if any number'}, {'start': '1054.880', 'end': '1061.280', 'text': 'is multiplied with any number then the same number comes again then 1 * 2 = 2 - 3iot Now minus and plus'}, {'start': '1061.280', 'end': '1068.880', 'text': 'minus 4 * 2 = 8iot Minus and minus plus 4 * 3 = 12 iot and iot if multiplied'}, {'start': '1068.880', 'end': '1073.200', 'text': 'then iot² Now we have both these likes going on'}, {'start': '1073.200', 'end': '1075.760', 'text': 'so'}, {'start': '1076.200', 'end': '1085.600', 'text': '2 - 3 and -8 will come -1iot and plus 12 * -1 will come because what is the value of iot² we'}, {'start': '1085.600', 'end': '1094.240', 'text': 'have -1 then we will have 2 - 11iot, we will have -12 so both of these'}, {'start': '1094.240', 'end': '1097.400', 'text': 'are real parts. If we write the real part on one side then it'}, {'start': '1097.400', 'end': '1105.919', 'text': 'will come from 2-12 -1iot 2 -2 -10 -10 -11iot This is'}, {'start': '1105.919', 'end': '1112.799', 'text': 'the answer to this, now here we have only'}, {'start': '1112.799', 'end': '1116.799', 'text': 'to multiply the imaginary number, in the part number seven we have the imaginary. multiply the number'}, {'start': '1116.799', 'end': '1120.320', 'text': 'We have to do it with complex number i.e. both'}, {'start': '1120.320', 'end': '1122.960', 'text': 'complex numbers with real and imaginary part, this is also a complex number and this'}, {'start': '1122.960', 'end': '1128.080', 'text': 'is also a complex number but here if we have to multiply the imaginary part then we'}, {'start': '1128.080', 'end': '1134.240', 'text': 'will get 8 * 2 = 16 plus and minus will come to minus because here there is plus when there'}, {'start': '1134.240', 'end': '1138.400', 'text': 'is no sign then it means that here plus is present then by multiplying'}, {'start': '1138.400', 'end': '1143.760', 'text': 'plus and minus the minus will come 8 * 2 = 16 and If iota is multiplied then we'}, {'start': '1143.760', 'end': '1149.440', 'text': 'will get iot². Now we will have 16. What will come in its place'}, {'start': '1149.440', 'end': '1155.240', 'text': '-16 and we have the value of square -1 then we will have'}, {'start': '1155.240', 'end': '1161.280', 'text': '16IOT + 16. This is also the answer which we have ok but if you guys have to give the order then'}, {'start': '1161.280', 'end': '1168.480', 'text': 'we will have 16 + 16iot. This is the answer which we have, this'}, {'start': '1168.480', 'end': '1175.520', 'text': 'is the real part and this is its imagined part, similarly 3 + In 2iot part number at,'}, {'start': '1175.520', 'end': '1182.000', 'text': 'we have 3 + 2iot² squared so square means'}, {'start': '1182.000', 'end': '1188.320', 'text': 'multiply 3+2iot twice i.e. 3 + 2iot * 3+ 2iot similarly you can multiply separately'}, {'start': '1188.320', 'end': '1195.120', 'text': 'or 3+ 2iot which we have is its whole square so you'}, {'start': '1195.120', 'end': '1199.400', 'text': 'can apply a+b² formula also so (a+b)² formula we have'}, {'start': '1199.400', 'end': '1206.400', 'text': 'a² + b² + 2ab This formula can also be applied, so we have'}, {'start': '1206.400', 'end': '1211.679', 'text': 'done this, now we apply this formula, then it will become equal to a², so'}, {'start': '1211.679', 'end': '1217.600', 'text': 'the bug of a, we have 3, then it will become 3², instead of plus b, if there is 2iot, then 2iot'}, {'start': '1217.600', 'end': '1222.400', 'text': 'will be squared and in the plus formula, we have two, it will come in its place,'}, {'start': '1222.400', 'end': '1229.280', 'text': 'instead of a, what we have is 3 and instead of b, what we have, is 2iot. So we'}, {'start': '1229.280', 'end': '1234.960', 'text': 'will get 3², we will get nine, plus 2², we will get 4, and'}, {'start': '1234.960', 'end': '1241.919', 'text': 'we will write the square of iota in its place, plus 2 * 3 = 6 and 6 * 2 = 12iot, we will get this'}, {'start': '1241.919', 'end': '1250.799', 'text': ', 9 + 4 * -1 -1, we put the value of iot² and this'}, {'start': '1250.799', 'end': '1256.159', 'text': 'will come to us, plus 12iot, so we will get 9 - 4 + 12iota, because plus and Minus'}, {'start': '1256.159', 'end': '1262.840', 'text': 'minus will come and 4 * 1 = 4. So if we subtract 4 from 9, we will get 5 plus'}, {'start': '1262.840', 'end': '1268.480', 'text': '12iot. This is our generalized form, general form of complex number. This'}, {'start': '1268.480', 'end': '1273.440', 'text': 'is our answer. Now this question and this one which'}, {'start': '1273.440', 'end': '1278.640', 'text': 'is first second fifth sixth and yes fifth and sixth part, this one and this one'}, {'start': '1278.640', 'end': '1283.440', 'text': 'are exactly the same. Now you have to multiply it with whom you have'}, {'start': '1283.440', 'end': '1289.360', 'text': "to multiply it, son. With this, let's go and solve it, 3 * 3 = 9."}, {'start': '1289.360', 'end': '1293.440', 'text': 'There is no need to expand because we have already'}, {'start': '1293.440', 'end': '1297.200', 'text': 'explained it very well. I hope you guys have understood. Now I'}, {'start': '1297.200', 'end': '1306.159', 'text': 'am directing it that 3 * 3 = 9 + 3 * 6 = 18 - 6 * 3 = 18 minus and plus - 6 * 6'}, {'start': '1306.159', 'end': '1308.320', 'text': '='}, {'start': '1309.000', 'end': '1319.000', 'text': '36². This will become 9 + 18. - 18iota This will cancel out -36 * -1 This will become 9 +'}, {'start': '1319.000', 'end': '1329.960', 'text': '36 = 45 This will give us the answer Now look in this, here we have -5'}, {'start': '1329.960', 'end': '1334.799', 'text': '-3iot We can make minus common from both, then we will get this.'}, {'start': '1334.799', 'end': '1341.520', 'text': 'If we make the minus common then 5 + 3iot Whole square, now this square'}, {'start': '1341.520', 'end': '1347.120', 'text': 'is on the minus and also on this, so it is your choice, now taken separately on this. We can also take it directly'}, {'start': '1347.120', 'end': '1351.520', 'text': ', there is no problem but now here we'}, {'start': '1351.520', 'end': '1355.039', 'text': 'will use the formula of plus, if we square in minus then it will become plus and'}, {'start': '1355.039', 'end': '1362.720', 'text': 'this is the whole square of 5 + 3iot, by the way the same thing has come 3 + 2iota 5 + 3iot is the same thing,'}, {'start': '1362.720', 'end': '1366.440', 'text': 'we will have 5²'}, {'start': '1366.440', 'end': '1372.280', 'text': '3iot² + 2 * ab a we have 5 and b we have'}, {'start': '1372.280', 'end': '1387.799', 'text': '3iot 25 + 9iot² + 2 5 10 and 10 * 3 = 30, we will get 25 + 9 *-1 +'}, {'start': '1387.799', 'end': '1396.080', 'text': '30, we will get 25 - 9 + 30 because plus and minus will come to minus'}, {'start': '1396.080', 'end': '1401.120', 'text': 'and by multiplying with one, 9 * 1 = 9, so we will subtract this n from 25,'}, {'start': '1401.120', 'end': '1409.600', 'text': 'then 16 + 30, this will be our answer,'}, {'start': '1409.600', 'end': '1414.720', 'text': 'part number 11. If we have to multiply this, then Multiply one with that and'}, {'start': '1414.720', 'end': '1417.840', 'text': 'then we have to multiply 2 with that,'}, {'start': '1417.840', 'end': '1422.600', 'text': 'so if we multiply one, we will get the same thing again 1 - 3'}, {'start': '1422.600', 'end': '1426.480', 'text': '[Music] Now it'}, {'start': '1426.480', 'end': '1431.120', 'text': 'is the turn of 2, so multiply 2 with this, we'}, {'start': '1431.120', 'end': '1435.360', 'text': 'will get plus 2, and if we multiply this with this, we will get plus and minus minus, we will get 2'}, {'start': '1435.360', 'end': '1440.480', 'text': '* 3 = 6, we will get aot and'}, {'start': '1441.960', 'end': '1450.200', 'text': 'aot², we will have one. We will write this with this -6'}, {'start': '1450.200', 'end': '1454.799', 'text': '² + 2 - 3'}, {'start': '1454.799', 'end': '1458.720', 'text': 'Just and only we have given the order, we have just shifted the real part here because minus'}, {'start': '1458.720', 'end': '1463.120', 'text': 'because iot² is equal to -1, so this will be the real part, we have that'}, {'start': '1463.120', 'end': '1470.799', 'text': 'part, this is what we will have 1 - 6 * -1 + 2'}, {'start': '1470.799', 'end': '1477.200', 'text': '- 3. If we have common the iota from both, then this will be the minus and the minus'}, {'start': '1477.200', 'end': '1481.760', 'text': 'plus will be 1 + 6 + 2'}, {'start': '1481.760', 'end': '1485.760', 'text': '- 3 and then we have imaginary'}, {'start': '1485.760', 'end': '1490.799', 'text': 'The part is done and we have this real part.'}, {'start': '1490.799', 'end': '1498.159', 'text': 'Now in question number two, part number 12 is what we have that 2 +iot and 2 -iot.'}, {'start': '1498.159', 'end': '1502.919', 'text': 'We also have the formula, so which one is the formula. We have the formula that'}, {'start': '1502.919', 'end': '1512.360', 'text': 'a+b * a- b and it is equal to a² -'}, {'start': '1512.360', 'end': '1517.600', 'text': 'b². Exactly in the same way, if we multiply it, then we'}, {'start': '1517.600', 'end': '1522.240', 'text': 'have done many equations which we have multiplied. Now here we have There is a new formula,'}, {'start': '1522.240', 'end': '1527.600', 'text': 'if we apply this formula then we have a + b and if it becomes ab then'}, {'start': '1527.600', 'end': '1533.760', 'text': 'it will be equal to a² - b² so instead of a we have 2 under the root then its square'}, {'start': '1533.760', 'end': '1540.240', 'text': 'and instead of minus b we have iot then the square of iot will become equal to this now'}, {'start': '1540.240', 'end': '1544.000', 'text': 'we have square and square root will cancel out so this'}, {'start': '1544.000', 'end': '1549.919', 'text': 'will be equal to 2 we have the value of minus iot² we have -1 so this will become equal to us Two'}, {'start': '1549.919', 'end': '1555.240', 'text': 'minus and minus plus one, so we have three, we'}, {'start': '1555.240', 'end': '1560.880', 'text': 'will get the answer to this, we have passed question number two, we have completed it, now we'}, {'start': '1560.880', 'end': '1565.440', 'text': 'move towards question number three, here I hope that'}, {'start': '1565.440', 'end': '1570.159', 'text': 'you have understood the lecture I have given till now, now whatever question you people have,'}, {'start': '1570.159', 'end': '1574.000', 'text': 'you can ask us.'}]