Chapter 9.7, Problem 2CFU

To determine

To describe how to square a complex number in polar form.

Answer to Problem 2CFU

The square of complex number in polar forms is $r^2{\left(\cos \theta +i\sin \theta \right)}^2$

Explanation of Solution

Given information

To square a complex number in polar form.

Formula used:

  $\left[x=r\cos \theta ,y=r\sin \theta \right]$

Calculation:

To Express square complex number in polar forms.

Let complex number will be $x+yi$

Then square of complex number will be ${\left(x+yi\right)}^2=\left(x+yi\right).\left(x+yi\right)$

Now to get complex number in polar forms

  $\begin{array}{l}{\left(x+yi\right)}^2=\\ ={\left(r\cos \theta +ir\sin \theta \right)}^2\left[x=r\cos \theta ,y=r\sin \theta \right]\\ =r^2{\left(\cos \theta +i\sin \theta \right)}^2\end{array}$

The square of complex number in polar forms is $r^2{\left(\cos \theta +i\sin \theta \right)}^2$