How to visualise $z=\cot\theta+i\cdot\tan\theta$ in complex-plane?

Question

What would be the graph of $z=\cot\theta+i\cdot\tan\theta$ in complex plane?

Answer 1

Writing $z=x+iy$ tells us it looks like the graph of $y=1/x$.

Answer 2

We have that by $t=\tan \theta \in \mathbb R$ since $\tan \theta=\frac1{\cot \theta}$ with $\theta \in\left(-\frac \pi 2, 0\right)\cup\left(0,\frac \pi 2\right)$

$$z=\frac1t+it$$

that is $y=\frac1x$.