Question

Convert the given complex number in polar form : $-3$

Answer 1

Given, $z=-3$
Let, $r\cos \theta =-3$ and $r\sin \theta =0$
On squaring and adding, we obtain
$r^2{\cos }^2\theta +r^2{\sin }^2\theta ={(-3)}^2$
$\Rightarrow r^2({\cos }^2\theta +{\sin }^2\theta )=9$
$\Rightarrow r^2=9$
$\Rightarrow r=\sqrt{9}=3$ (Conventionally $r>0$ )
$\therefore 3\cos \theta =-3$ and $3\sin \theta =0$
$\Rightarrow \cos \theta =-1$ and $\sin \theta =0$
$\therefore \theta =\pi$
So, the polar form is
$\therefore -3=r\cos \theta +ir\sin \theta =3\cos \pi +3\sin \pi =3\left(\cos \pi +i\sin \pi \right)$