Question

Find the modulus and the arguments of each of the complex no of the following
Z= -1- i 3^1/2

Answer 1

$z=-1-i \sqrt{3} \\ \\|z|= \sqrt{(-1)^2+( \sqrt{3})^2 }= \sqrt{1+3}= \sqrt{4}=2\\ \\ \phi=cos^{-1}( \frac{-1}{2} )= \frac{2 \pi }{3}\ or\ \frac{4 \pi }{3}$

But z is in the third quadrant. So $\phi= \frac{4 \pi }{3}$