Answer
$ -\frac{25\sqrt 2}{2}+\frac{25\sqrt 2}{2}i$
Work Step by Step
Based on the given conditions, we have:
$[\sqrt 5(cos\frac{3\pi}{16}+i\ sin\frac{3\pi}{16})]^4\\ =25(cos\frac{3\pi}{4}+i\ sin\frac{3\pi}{4})\\ =25(-\frac{\sqrt 2}{2}+i\frac{\sqrt 2}{2})\\ =-\frac{25\sqrt 2}{2}+\frac{25\sqrt 2}{2}i$
