Question

Represent the complex number $z=1+i$in polar form$?$

Answer 1

Representing the given complex number in polar form.

Given,$z=1+i$

$z=1+i=\sqrt{2}\left(\frac{1}{\sqrt{2}}+i\frac{1}{\sqrt{2}}\right)....\left(1\right)$

Let the polar form of the given equation be $z=r\cos \theta +ir\sin \theta ....\left(2\right)$

Comparing $\left(1\right)and\left(2\right)$

We get ,$r=\sqrt{2}$ and $\theta =\frac{\pi }{4}$$[\cos 45°=\sin 45°=\frac{1}{\sqrt{2}}]$

Thus, the polar form is $z=\sqrt{\mathbf{2}}\mathbf{}\mathbf{(}\mathit{c}\mathit{o}\mathit{s}\frac{\mathbf{}\mathbf{\pi }}{\mathbf{4}}\mathbf{+}\mathbf{}\mathit{i}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{}\frac{\mathbf{\pi }}{\mathbf{4}}\mathbf{}\mathbf{)}\mathbf{.}$