Question

Express the following complex number in the polar form
$\frac{1+i}{1-i}$

Answer 1

Given,

$\frac{1+i}{1-i}$

$\frac{1+i}{1-i}\times \frac{1+i}{1+i}$

$=\frac{1-1+2i}{2}$

$z=0+i$

$r=\sqrt{0^2+1^2}=1$

$\theta ={\tan }^{-1}\frac{1}{0}=\frac{\pi }{2}$

$z=1(\cos \frac{\pi }{2}+i\sin \frac{\pi }{2})$