I encountered this problem in my exercise set, and was stumped.
Solve (z + 1)^4 = 1 - i
My approach to the problem was to recognize that (1 - i) could be rewritten as [ (1 - i)^4 ] / 8.
Which then gives..
(z + 1)^4 = (1 - i)^4 / 8
(z + 1) = +/- (1 - i) / 4throot(8)
But I'm not sure how to proceed from here, since it would appear that in solving each of the resulting two equations, I would only obtain two roots, rather than the expected four.
Edit: Sorry, but LaTeX kept giving me an error when I tried using it.