Home > PC3 > Chapter 11 > Lesson 11.2.4 > Problem11-129

11-129.

Given $z_1 = 12(\cos(\frac { \pi } { 3 }) + i \sin(\frac { \pi } { 3 }))$ and $z_2 = 4(\cos(\frac { 4 \pi } { 3 }) + i \sin(\frac { 4 \pi } { 3 }))$, compute each of the following values.

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

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

3. ${z_1}^{2}$

Compute $z_{1} · z_{1}$.

Products and Quotients of Complex Numbers in Polar Form

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 $z_1z_2 = r_1r_2(\cos(a + b) + i \sin(a + b))$.

The quotient of the two numbers is $\frac { z _ { 1 } } { z _ { 2 } } = \frac { r _ { 1 } } { r _ { 2 } }(\cos(a − b) + i \sin(a − b))$.