So it's obvious geometrically that the argument of $z=i$ is $\pi/2$.
However the method of getting the argument is $\arctan(y/x)$. And when in the case of $z=i$, $y/x = 1/0$ which is undefined...
So when you want to find the argument of a complex number is this the correct process -
- $\operatorname{Argument}(z) = \arctan(y/x)$ if $x\neq0$.
- If $x = 0$, then $\operatorname{Argument}(z) = \pi/2\text{ or }-\pi/2$
Is that the way I should be approaching it?