Chapter 14.4, Problem 22WE

To determine

To find: The given complex number in polar form.

Answer to Problem 22WE

  $13\left(\cos {22.6}^0+i\sin {22.6}^0\right)$ .

Explanation of Solution

Given information:

A complex number is given as $12+5i$ .

Concepts used: The polar form of a complex number $z=x+yi$ is given by −

  $z=r\left(\cos \theta +i\sin \theta \right)$

where $r=\sqrt{x^2+y^2},\cos \theta =\frac{x}{r},\sin \theta =\frac{y}{r}$ .

Calculation:

Given complex number in polar form is $12+5i$ .

Converting into polar form -

  $\begin{array}{l}12+5i\\ r=\sqrt{x^2+y^2}=\sqrt{{\left(12\right)}^2+{\left(5\right)}^2}=13\\ \cos \theta =\frac{x}{r}=\frac{12}{13}\\ \Rightarrow \theta ={22.6}^0\\ \sin \theta =\frac{y}{r}=\frac{5}{13}\\ \Rightarrow \theta ={22.6}^0\end{array}$

Hence, given complex number in desired form is $13\left(\cos {22.6}^0+i\sin {22.6}^0\right)$ .