How to add consecutive imaginary numbers

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?

Re: How to add consecutive imaginary numbers

Quote:

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?

Re: How to add consecutive imaginary numbers

Sorry, what does that 'E' symbol mean and what are the variables equal to? And the 'mod 4' part?

Re: How to add consecutive imaginary numbers

Re: How to add consecutive imaginary numbers

Quote:

Originally Posted by

**daigo** Sorry, what does that 'E' symbol mean and what are the variables equal to? And the 'mod 4' part?

If it helps:

you can think of clocks being mod 12. We know that 13:00 is 1pm, 16:00 is 4pm etc., We say that the numbers are equal if they differ by 12. So 13 = 1 mod 12, and 16=4 mod 12.

Similarly, when working with degrees often we operate mod 360. So you would say that 380 degrees = 20 degrees. This is because 380=20 mod 360!

Re: How to add consecutive imaginary numbers

Quote:

Originally Posted by

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