Question

Find the modulus & argument of the following.
$-1-i\sqrt{3}$.

Answer 1

Given,

$z=-1-i\sqrt{3}=a+ib$

modulus: $|z|=\sqrt{a^2+b^2}=\sqrt{(-1{)}^2+(-\sqrt{3}{)}^2}=2$

argument: $\theta ={\tan }^{-1}\left(\frac{b}{a}\right)={\tan }^{-1}\left(\frac{-\sqrt{3}}{-1}\right)=\frac{\pi }{3}$