CPM Homework Help : PC3 Problem 13-66

Let $w=5\left(\cos\left(\frac{\pi}{3}\right)+i\sin\left(\frac{\pi}{3}\right)\right)$ and $z=2\sqrt{2}\left(\cos\left(\ \frac{5\pi}{4}\right)+i\sin\left(\frac{5\pi}{4}\right)\right)$ . Compute:

$zw$

$\frac { w } { z }$

Hint:

$\left. \begin{array} { l } {\text{Given two complex numbers } z _ { 1 } = r _ { 1 } ( \operatorname { cos } ( a ) + i \operatorname { sin } ( a ) ) \text { and } z _ { 2 } = r _ { 2 }( \operatorname { cos } ( b ) + i \operatorname { sin } ( b ) ) }. \\ { \text {The product of the two numbers is } z _ { 1 } z _ { 2 } = r _ { 1 } r _ { 2 } ( \operatorname { cos } ( a + b ) + i \operatorname { sin } ( a + b ) ) } \\ { \text {The quotient of the two numbers is } \frac { z _ { 1 } } { z _ { 2 } } = \frac { r _ { 1 } } { r _ { 2 } } ( \operatorname { cos } ( a - b ) + i \operatorname { sin } ( a - b ) ) } \end{array} \right.$