### Home > PC3 > Chapter 12 > Lesson 12.2.1 > Problem12-95

12-95.

Given $z_1 = 6\Big[\cos(\frac { 7 \pi } { 12 }) + i \sin(\frac { 7 \pi } { 12 })\Big]$ and $z_2 = 3 \Big[\cos(\frac { \pi } { 4 }) + i \sin (\frac { \pi } { 4 })\Big]$ compute each of the following values. Write your answers in $a + bi$ form.

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