Linear Algebra - Finding values

Question

Find all the values of the sixth root for the following: (-1-i)^1/6

Answer 1

(-1 - i)^1/6 = {√2[cos(225° + 360°n) + isin(225° + 360°n)]}^1/6} = 2^1/12[cos(36.5° + 60ˆn) + isin(36.5° + 60°n)].

By giving n = 0, 1, 2, 3, 4, 5 in last expression we get values of this six root.