### Home > PC3 > Chapter 12 > Lesson 12.1.2 > Problem12-30

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:

1. $z_{1}z_{2}$

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 $z _ { 1 } z _ { 2 } = r _ { 1 } r _ { 2 } ( \operatorname { cos } ( a + b ) + i \operatorname { sin } ( a + b ) )$

1. $\frac { z 1 } { z _ { 2 } }$

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 $\frac { z _ { 1 } } { z _ { 2 } } = \frac { r _ { 1 } } { r _ { 2 } } ( \operatorname { cos } ( a - b ) + i \operatorname { sin } ( a - b ) )$