Question

Find the polar form of (4sqrt(3)i-4)^200

Answer 1

Use DeMoivre's theorem:\[(r(\cos\theta+i\sin \theta))^n=r^n (\cos n \theta + i \sin n \theta )\]The trick is now just to find \(r\) and \(\theta\).\[4\sqrt 3i-4=r(\cos \theta+i\sin\theta) \Rightarrow \left\{ \begin{array}{l}r=\cdots\\\theta = \cdots \end{array} \right.\]