# How do you simplify (5i)(-8i)?

May 14, 2018

$\text{ }$
color(blue)((5i)*(-8i)=40

#### Explanation:

$\text{ }$

A Complex Number is a combination of a Real Number and an Imaginary Number.

Standard Form of a Complex Number is : color(red)(a+bi, where

color(red)(a is the Real Part and color(red)(b is the Imaginary Part.

In the problem given, the Real Part is unavailable.

You have just the Imaginary Part for both the complex numbers.

Multiply the complex numbers color(blue)((5i)*(-8i) :

$\left(5 i\right) \cdot \left(- 8 i\right)$

Multiply the numerical constants first with the sign:

$5 \cdot \left(- 8\right)$

rArr color(red)((-40)

You need this intermediate result in the final step.

Next, multiply $i$ by $i$.

In complex numbers, color(blue)(i = sqrt(-1)

Hence,

$i \cdot i = \sqrt{- 1} \cdot \sqrt{- 1}$

$\Rightarrow {i}^{2} = {\left[\sqrt{- 1}\right]}^{2}$

In radicals arithmetic, color(red)(sqrt(a^2)=sqrt(a*a)=a

$\Rightarrow {i}^{2} = \left(- 1\right)$

Hence,

color(blue)((5i)(-8i)=[-40*(-1)]=40

Hope it helps.
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