How to solve (-1-i)^(1/6) ?

Question

(-1-i)^(1/6), in other words, the sixth root of -1-i. Leave answers in polar form.

Answer 1

Represent the complex number (-1-i) as z = √2(cis (225^o + k360^o) and then use deMoivre's theorem;

z^(1/6) = 2^(1/12) cis (225/6 + 60k)   where the angle is in degrees and k takes on values 0 through 5 to produce all six of the sixth roots of z = (-1-i).