Answer
(a) $ 4cos270^\circ+4i\ sin270^\circ$,
(b) $ 2cos300^\circ+2i\ sin300^\circ$,
(c) $ \sqrt {10}cos198.4^\circ+\sqrt {10}i\ sin198.4^\circ$
Work Step by Step
(a) $-4i=4(0-i)=4(cos270^\circ+i\ sin270^\circ)=4cos270^\circ+4i\ sin270^\circ$,
(b) $1-i\sqrt 3=2(\frac{1}{2}-i\ \frac{\sqrt 3}{2})=2(cos300^\circ+i\ sin300^\circ)=2cos300^\circ+2i\ sin300^\circ$,
(c) $-3-i=\sqrt {10}(-\frac{3\sqrt {10}}{10}-i\ \frac{\sqrt {10}}{10})=\sqrt {10}(cos198.4^\circ+i\ sin198.4^\circ)=\sqrt {10}cos198.4^\circ+\sqrt {10}i\ sin198.4^\circ$
