Third
Our next function is actually not too fancy.
It is the tangent function.
\(f(z) = \tan\,z = \dfrac{\sin\,z}{\cos\,z},\quad z \in \mathbb{C}(0,3)\)
How could one recognise it simply by looking at the picture? (And when possible knowing that it is periodic.) Again it would be worth to examine the real axis…