Chapter 9.3, Problem 6AYU

When a complex number $z$ is written in the polar form $z\text{ = }r(cos\theta \text{ + }i\sin \theta )$, the nonnegative number $r$ is the _____ or _____ of $z$, and the angle $\theta$, $0\le \theta \text{ < 2}\pi$, is the _____ of $z$.

To determine

To fill: When a complex number $z$ is written in the polar form $z = r\left(\text{cos} \theta + i\text{sin} \theta \right)$, the nonnegative number $r$ is the _____ or _____ of $z$, and the angle $\theta$, $0\le \theta \le 2\pi$, is the ____ of $z$.

Answer to Problem 6AYU

Solution:

Magnitude; modulus; argument.

Explanation of Solution

When a complex number $z$ is written in the polar form $z = r\left(\text{cos} \theta + i\text{sin} \theta \right)$, the nonnegative number $r$ is the magnitude or modulus of $z$, and the angle $\theta$, $0\le \theta \le 2\pi$, is the argument of $z$.