Question

Convert the given complex number in polar form: -3

Answer 1

z = -3
Let $rcos\theta =-3andrsin\theta =0$
On squaring and adding, we obtain
$r^{2}co{s}^2\theta +r^{2}si{n}^2\theta =(-3{)}^2\Rightarrow r^2(co{s}^2\theta +si{n}^2\theta )=9\Rightarrow r^2=9\Rightarrow r=\sqrt{9}=3[Conventionally,r>0]\therefore 3cos\theta =-3and3sin\theta =0\Rightarrow cos\theta =-1andsin\theta =0\therefore \theta =\pi \therefore -3=rcos\theta +irsin\theta =3cos\pi +i3sin\pi =3(cos\pi +isin\pi )$
This is the required polar form.