Question

Given that i^2 = −1, for how many integers n is (n + i)^4 an integer?

Answer 1

:|

Answer 2

Well I guess there are a couple ways to try to handle this, the easiest might be just to expand the (n+i)^4 out by multiplication remember:

\[(n+i)^4=(n+i)*(n+i)*(n+i)*(n+i)\]

then after you multiply that together you'll have a polynomial with real and imaginary parts. Solve so that the imaginary part = 0. Give it a go, I'll help you out.

Answer 3

I figured it out to be 3.

Answer 4

by graphing