Question:

How do you add imaginary numbers?
The question is as follows: The imaginary number i is defined such that i^2 (I can't make small numbers for powers so ^ will do :P) = -1. What does i + i^2 + i^3 + ... + i^49 equal? I know the answer as I have an answer sheet I'm intrested as to how you arrive at the answer.

Answers:

A-Best: i is sqrt(-1) = i i^2 is [sqrt(-1)]^2 = -1 i^3 is [sqrt(-1)]^3 = -1 * i = -i i^4 is [sqrt(-1)]^4 = -1 * -1 = 1 So if you add just the first four, you get i + (-1) + (-1) + 1 = 0. The i's cancel out and so do the 1's. (Adding i terms is just like adding any other variable - just add the coefficients!) So for i^5 through i^8, you'd get 0 (the cycle repeats itself, so that i^5 is the same as i, i^6 is the same as i^2, etc.). And for i^9 through i^12 you get 0. And so on until you get to i^48. That leaves you with i^49, which simplifies to i. So the sum of all of these is i.  

A: you use an imaginary calculator  

A: Imaginary numbers were always my Achilles heel in math, but do you add the imaginary and real parts separately?