Originally Posted by

**daigo** What is i + i^2 + i^3 + ... + i^49?

I know for each one there is only 4 possibilities of solutions, i, -i, 1, and -1. So I divided 49 by 4 and got 12.25 so there's 12 of each solution plus one extra one. So I did: 12i + -12i + 12 + -12 and then the 49th term I think is i but I'm not sure because I forgot what the value is (calculator is not allowed). So everything cancels out and I'm just left with i as the last term...But I don't think the solution is i because I don't think I did it correctly.

What if I were told to add up every other consecutive one starting from i? Like i + i^3 + i^5 + ... i^49?