Question

Convert the given complex number into the polar form:$z=-3$

Answer 1

$z=-3+0i$

putting

$-3=r\cos \theta ,0=r\sin \theta$

$9+0=r^2({\sin }^2\theta +{\cos }^2\theta )$

$r^2=9$

$r=3$

$\frac{r\sin \theta }{r\cos \theta }=\frac{0}{-3}$

$\tan \theta =0$

$\theta =0$

So, $|z|=3$, argument of $z=0$

Therefore, polar form of $z$ is

$z=r(\cos \theta +i\sin \theta )$

$=3(\cos 0^{\circ }+i\sin 0^{\circ })$