Question

Express the complex number $z=-1+\sqrt{2}i$ in polar form.

Answer 1

$z=-1+\sqrt{2}i$
$\left|z\right|=\sqrt{{(-1)}^2+{\left(\sqrt{2}\right)}^2}=\sqrt{1+2}=\sqrt{3}$
$Argz=\pi -{\tan }^{-1}\left(\frac{\sqrt{2}}{1}\right)=\pi -{\tan }^{-1}\left(\sqrt{2}\right)=\theta$ (say)
$\therefore$ $z=\sqrt{3}(\cos \theta +i\sin \theta )$ where $\theta =\pi -{\tan }^{-1}\sqrt{2}$