Question

When a complex number z is written in the polar form

$z=r(\cos \theta +i\sin \theta )$, the nonnegative number r is the______

or ________ of z, and the angle$\theta ,0\le \theta \le 2\mathrm{\pi }$

is the_________ of z.

Short answer

modulus , magnitude and argument of z.

Step-by-step solution

Step 1. Given

polar form$z=r(\cos \theta +i\sin \theta )$.

$\theta ,0\le \theta \le 2\mathrm{\pi }$

Step 2. Explanation

Consider

$z=r(\cos \theta +i\sin \theta )$is the complex number in polar form where r is called the modulus $\theta$is the argument .