This is my first time here, so I'm not sure if this question belongs here or somewhere else. I'm actually in Year 11, but none of the pre-university topics seemed to cover this, so sorry if I posted this in the wrong place:

Show that the roots of (z-1)^4 + (z+1)^4 = 0 are +/- i cot (pi/8) and +/- i cot (3pi/8)

Thanks