Question

Convert $Z=\frac{-1+i}{\sqrt{2}}$. in polar form.

Answer 1

$Z=\frac{-1+i}{\sqrt{2}}=(-\frac{1}{\sqrt{2}}+i\frac{1}{\sqrt{2}})...........\left(1\right)$
Let Polar form of Given Equation be $Z=rcos\theta +irsin\theta ...............\left(2\right)$
Comparing (1) and (2)
we can write,
$rcos\theta =-1\ast \frac{1}{\sqrt{2}}=1\ast \cos {135}^{o}rsin\theta =1\ast \frac{1}{\sqrt{2}}=1\ast \sin {135}^o$
$\therefore Z=\cos {135}^o+i\sin {135}^o$