Question

Represent the complex number $Z=-1+i$. in polar form.

Answer 1

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