Simplify (1+iroot3)^9 + (1-iroot3)^9 in x+iy form

Answer 1

1 + √3 i = 2 cis π/3
so, (1 + √3 i)^9 = 2^9 cis (9 * π/3) 512 cis 3π = -512
Now do the other.