Answer
See the explanation below.
Work Step by Step
The polar form of a complex number is yet another form to represent a complex number, other than rectangular form.
A complex number $z=a+ib$ can be represented in polar form as:
$z=r\left( \cos \theta +i\sin \theta \right)$
Here $a=r\cos \theta $, $b=r\sin \theta $, $r=\sqrt{{{a}^{2}}+{{b}^{2}}}$ and $\tan \theta =\frac{b}{a}$
The values $r$ and $\theta $ are called the modulus and argument of a complex number $z$ respectively, with $0\le \theta \le 2\pi $.
Example:
The above explanation can be justified with the help of an example. The provided complex number $z=5\left( \cos 30{}^\circ +i\sin 30{}^\circ \right)$ is in simple polar form.The modulus and argument of a complex number is $5$ and $30{}^\circ $ respectively. Simplify the complex number,
$\begin{align}
& z=5\left( \cos 30{}^\circ +i\sin 30{}^\circ \right) \\
& =5\left( \frac{\sqrt{3}}{2}+i\frac{1}{2} \right) \\
& =\frac{5\sqrt{3}}{2}+i\frac{1}{2}
\end{align}$
The real part of a complex number is $\frac{5\sqrt{3}}{2}$ and the imaginary part of a complex number is $\frac{1}{2}$.
The above expression of a complex number in polar form is converted into rectangular form.
