What is the simplified result of the expression -2i(3-4i+8i squared)

Question

terenzreignz · Answer

Let's kill the ambiguity... is this what it looks like...
$$\Large -2i(3-4i+8i^2)$$
?

anonymous · Answer

Yes I didn't know how to type the square in the formula

terenzreignz · Answer

Okay, so, first things first, you know that...
$$\large i^2 = -1$$right?

anonymous · Answer

nope

terenzreignz · Answer

Seriously? :/
Well anyway, i is defined as such....
$$\Large i = \sqrt{-1}$$
So it only makes sense that...
$$\Large i^2 = -1$$

anonymous · Answer

I haven't done this kind of math in 30 years...I'm trying to relearn for a certification test. And during my long career I truly did not use this. :)

terenzreignz · Answer

Understood, sir/madame...
so, granted, and accepted that 
$$\Large i^2 = -1$$

We have an occurrence of $\large i^2$  right here...
$$\Large -2i(3-4i+8\color{red}{i^2})$$

So that may be replaced by its equivalent (equal) -1... like so...
$$\Large -2i(3-4i+8\color{blue}{(-1)})$$

anonymous · Answer

oh ok

terenzreignz · Answer

So simplifying yields...
$$\Large -2i(3-4i\color{green}{-8})$$

These two terms may be combined into one...
$$\Large -2i(\color{orange}3-4i\color{orange}{-8})$$

$$\Large -2i(\color{blue}{-5}-4i)$$
At which point, all that's left is distributing the -2i

terenzreignz · Answer

Good luck with your certification test :)

anonymous · Answer

oh that makes so much sense now...thank you!!! Lynn

terenzreignz · Answer

No problem, Lynn :)
The name's Terence, at your service :D

anonymous · Answer

Thanks again.