Chapter 9.3, Problem 14AYU

To determine

To plot: Each complex number in the complex plane and write it in polar form. Express the argument in degrees.

Answer to Problem 14AYU

Solution:

$z=2\left(\text{cos}300°+i\text{sin}300°\right)$

Explanation of Solution

Given:

$1-\sqrt{3}i$

Calculation:

$r=\sqrt{x^2+y^2}=\sqrt{{\left(1\right)}^2+{\left(-\sqrt{3}\right)}^2}=\sqrt{4}=2$

The angle $\theta$, $0\le \theta \le 2\pi$, that satisfies both equations is $\theta =300°$ and $r=2$.

$z=r\left(\text{cos}\theta +i\text{sin}\theta \right)=2\left(\text{cos}300°+i\text{sin}300°\right)$