Answer to Question #320212 in Complex Analysis for Simon

Question

Z= - 220 sqrt (3) + 220i write in exponetial form

Answer 1

$Z=-220\sqrt{3}+220i=220\left( -\sqrt{3}+i \right) =220\cdot 2\left( -\frac{\sqrt{3}}{2}+\frac{1}{2}i \right) =\\=440\left( \cos \frac{5\pi}{6}+i\sin \frac{5\pi}{6} \right) =440\exp \left( \frac{5\pi}{6}i \right)$