Education

# Learn additive and multiplicative inverse easily

In maths, we study a lot of concepts that are useful for us. Multiplying and addition are words that every individual has heard about. These are basic operations that can be applied to two or more operands. There are various properties that have been exhibited by these two operations. In this article, we will be discussing additive inverse and multiplicative inverse.

The additive inverse of a number is described in mathematics as a value that, when added to the original number, yields the result 0. Unary minus, i.e. – p, represents the additive inverse of the original number ‘p.’ For example, because 29 − 29 = 0, the additive inverse of 29 is -29. The additive inverse is sometimes referred to as the opposite number, sign change, and negation. It alters the sign of a real number. The additive inverse of a positive value is always a negative number, whereas the additive inverse of a negative is always a positive number. The numeral ‘0’ is the only number whose additive inverse is 0 only, that is number itself is its inverse. As a result, the additive inverse of the number 0 is zero.

A complex number is defined as the sum of two real numbers, ‘a’ and ‘bi.’ As a result, the complex number Z may be represented as a sum of the real and imaginary numbers a and bi. As a result, Z = a + bi To calculate the additive inverse of Z, we must first discover a number z’ that, when added to z, yields the result 0.

A rational number’s additive inverse is the same original number with the opposite sign. The additive inverse of 2/3, for example, is – 2/3. By multiplying the original number by -1, we may find the additive inverse of a rational number. The additive inverse of 16/7, for example, is 16/7 * -1 = -16/7.

The multiplicative inverse of a number is a number that equals one when multiplied by the original number. The original number must never be equal to zero in this case. X-1 or 1/X represents the multiplicative inverse of a number X. A number’s multiplicative inverse is also known as its reciprocal. Inverse Multiplication Example Multiplicative Inverse of One: Because 1×1=1, the multiplicative inverse of one equals one. Multiplicative Inverse of Zero: There is no multiplicative inverse of zero. This is due to the fact that 0xN=0 and 1/0 are undefined.

Inverse Multiplication Of A Complex Number 1/(x+yi) is the multiplicative inverse of any complex number x+yi. x and y are rational integers in this multiplicative inverse, and I am a radical. We must constantly remember to rationalise the multiplicative inverse in this scenario. There should be no radicals in the denominator of our final solution. Rationalisation: To rationalise 1/(x+yi), multiply the numerator and denominator with (x-Yi). You’ll get (x-yi)/(x2-(yi)2) as a result. We obtain a constant whole number in the denominator and radicals in the numerator when we conduct this operation with numbers instead of variables. Our multiplicative inverse is rationalised at this point.

If X-1 or 1/X is X’s multiplicative inverse, then X is X’s multiplicative inverse. This is due to multiplication’s commutative property, which stipulates that the result does not change if the order of the numbers is changed. One is known as the multiplicative identity because when multiplied by itself, the outcome is itself.

In the above article, we have discussed both additive inverses as well as multiplicative inverse in detail. This article will definitely help students to grasp these topics in detail. Students can even take the help of online platforms to understand these topics. One of the best online platforms to choose for the study is Cuemath.

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