The imaginary number i is defined such that i2 = –1. What does i + i2 + i3 + L + i 23 equal?
A. i
B. –i
C. –1
D. 0
E. 1
I’m sorry, there shouldn’t be any “L”, just “…” mark
6 Answers

You should memorize this pattern:
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 nonmultiples 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.

What is the L standing for? Should this just be a series adding all powers of i from 1 to 23? If so then
i^2 = 1
i^3 = i
i^4 = 1
So i + i^2 + i^3 + i^4 = 0
The same will happen with each succeeding set of four powers. This leaves you with i^21 + i^22 + i^23.
Can you finish it from there?

Define Imaginary Numbers

Imaginary Number Definition

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=(1 – i^24)/(1 – i) – 1 (geometric series formula) =0 – 1 = – 1 because i^24 = (i^4)^6 = ((i²)²)^6 = ((1)²)^6 = 1^6 = 1

= 1 + L i ,assuming i 23 means i^23. Have no idea what L is.