# Find the modulus and the principal argument of $-2i$

Let, $z=0+(-2i)$

$\therefore$ mod of $z=2$

But, I am getting stuck over here and I am unable to find the argument as the $\tan\alpha$ comes out to be not defined.

Any hint or help would be much appreciated.

Rather than just approaching it with a formula think about it graphically. Where is $-2i$ located on an Argand diagram?
It is on the vertical axis below the origin. Thus the argument is $-\frac{\pi}{2}$.