CPM Homework Help : PC3 Problem 12-30

Let $z_1 =$ $7\Big[\cos(\frac { 5 \pi } { 4 }) + i \sin(\frac { 5 \pi } { 4 })\Big]$ and $z_2 =$ $4\Big[\cos(\frac { \pi } { 3 }) + i \sin(\frac { \pi } { 3 })\Big]$ . Evaluate:

$z_{1}z_{2}$
Hint (a):
Given two complex numbers $z_1=r_1(\cos(a)+i\sin(a))$ and $z_2=r_2(\cos(b)+i\sin(b))$ , the product of the two numbers is $z _ { 1 } z _ { 2 } = r _ { 1 } r _ { 2 } ( \operatorname { cos } ( a + b ) + i \operatorname { sin } ( a + b ) )$

$\frac { z 1 } { z _ { 2 } }$
Hint (b):
Given two complex numbers $z_1=r_1(\cos(a)+i\sin(a))$ and $z_2=r_2(\cos(b)+i\sin(b))$ , the quotient of the two numbers is $\frac { z _ { 1 } } { z _ { 2 } } = \frac { r _ { 1 } } { r _ { 2 } } ( \operatorname { cos } ( a - b ) + i \operatorname { sin } ( a - b ) )$