Find the modulus and principal argument of `-2i`

Explanation

`z=-2i` when `z=a+bi` then, `a=0` and `b=-2`

`abs(z)=sqrt(a^2+b^2)=2`

`tan alpha= abs(frac{Im(z)}{Re(z)})=abs(frac{-2}{0})=`not defined=`oo`

`alpha= frac{pi}{2}`

`arg(z)=theta=>oo=frac{pi}{2}`

`theta` is a principal argument that lies between `(-theta, theta].`