Answer
$ -4+4i$
Work Step by Step
Based on the given conditions, we have:
$(1-i)^5\\ =[\sqrt 2(cos\frac{7\pi}{4}+i\ sin\frac{7\pi}{4})]^5\\ =4\sqrt 2(cos\frac{35\pi}{4}+i\ sin\frac{35\pi}{4})\\ =4\sqrt 2(cos\frac{3\pi}{4}+i\ sin\frac{3\pi}{4})\\ =4\sqrt 2(-\frac{\sqrt 2}{2}+\frac{\sqrt 2}{2}i)\\ =-4+4i$
