Chapter 6, Problem 40CLT

To determine

To write: The complex number in the standard form.

Answer to Problem 40CLT

The complex number in the standard form is $-9+i3\sqrt{3}$.

Explanation of Solution

Given information:

The given complex number is,

  $6\sqrt{3}\left(\cos \frac{5\pi }{6}+i\sin \left(\frac{5\pi }{6}\right)\right)$

The complex number in the standard form is written as,

  $\begin{array}{c}6\sqrt{3}\left(\cos \frac{5\pi }{6}+i\sin \left(\frac{5\pi }{6}\right)\right)=6\sqrt{3}\left(-\frac{\sqrt{3}}{2}+i\frac{1}{2}\right)\\ =-9+i3\sqrt{3}\end{array}$

Therefore, the complex number in the standard form is $-9+i3\sqrt{3}$.