Question

Express $\frac{-1+i}{\sqrt{2}}$ in the polar form

Answer 1

$\frac{-1+i}{\sqrt{2}}=r\left(\cos \theta +i\sin \theta \right)$

$r\cos \theta =d\frac{-1}{\sqrt{2}}$

$r\sin \theta =\frac{1}{\sqrt{2}}$

$\tan \theta =-1$

$\theta =\frac{3\pi }{4}$

$r^2=\frac{1}{2}+\frac{1}{2}$

$r^2=1$

$r=1$

$So,polarformof\frac{-1+i}{\sqrt{2}}is\left(1,\frac{3\pi }{4}\right).$