### Question Description

i dont understand the imaginary numbers stuff.

## Explanation & Answer

Thank you for the opportunity to help you with your question!

i^1 = i

i^2 = -1

i^3 = -i

i^4 = 1

And it will keep going as i, -1, -i, 1, i, -1, -i, 1, etc. So any exponent that's a multiple of 4 will equal 1, and you can figure out the values of non-multiples by counting up or down from the multiple of 4.

So onto the your math problem!

i = i

i^2 = -1

i^3 = -i

L = huh?

i^23 = -i (i^24 is 1. One number before that in the pattern is -i).

I have no idea what the "L" means, so I will ignore it. If it's a typo, hopefully you will understand how to do it on your own. It will be pointless for me to continue, since the answer will be different from your choices. But....

i + i^2 + i^3 + i^23 = i - 1 - i - i

= -i - 1

Just add whatever L is supposed to be. And there's your answer