Question

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

Answer 1

`" "`
`color(blue)((5i)*(-8i)=40`

Explanation:

`" "`

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)` :

`(5i)*(-8i)`

Multiply the numerical constants first with the sign:

`5*(-8)`

`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*i = sqrt(-1)*sqrt(-1)`

`rArr i^2=[sqrt(-1)]^2`

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

`rArr i^2=(-1)`

Hence,

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

Hope it helps.