Chapter 9.7, Problem 33E

To determine

To express the given complex number in polar form.

Answer to Problem 33E

  $5-12i=13\left(\cos \left(5.11\right)+i\sin \left(5.11\right)\right)$

Explanation of Solution

Given:

The given complex number is $5-12i$ .

Calculation:

Determine $r=\sqrt{x^2+y^2}$

  $r=\sqrt{{\left(5\right)}^2+{(-12)}^2}=13$

Now, determine $\theta =\arctan \left(\frac{y}{x}\right)+2\pi$

  $\begin{array}{l}\theta =\arctan \left(\frac{-12}{5}\right)+2\pi \\ \theta =5.11\end{array}$

So, the polar will be as follows

  $5-12i=13\left(\cos \left(5.11\right)+i\sin \left(5.11\right)\right)$