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

11-129.

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

MATH NOTES

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

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

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

1. $z_1^{\ 2}$

Compute $z_1·z_1$.