Question

Find the modulus are arguments $z=-\sqrt{3}+i$

Answer 1

$z=-\sqrt{3}+i$

Modulus

$\left|z\right|=\sqrt{(-\sqrt{3}{)}^2+1^2}$

$=\sqrt{3+1}$

$=2$

$\left|z\right|=2$

Argument

$\theta ={\tan }^{-1}\frac{b}{a}$

$={\tan }^{-1}\frac{1}{-\sqrt{3}}$

$=-30$

$\therefore \theta =180-30=150$

$\theta =150\times \frac{\pi }{180}$

$\theta =\frac{5\pi }{6}$