# The imaginary number i is defined such that i2 = –1. What does i + i2 + i3 + L + i 23 equal?

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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

• 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 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

• 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

• For the best answers, search on this site https://shorturl.im/W84dx

=(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.

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