Here is a picture of the function arctan(z) on the domain
D=C\{iy: |y| \ge 1}. It is a "branch" of the inverse to the function
tan(z) with value 0 at z = 0. The formula used to generate this
picture is
arctan(z)= (1/2)log((1+iz)/(1-iz))
The image of D by the map (1+iz)/(1-iz) is the slit plane:
C\(-infty,0] and then the principal branch of the logarithm is
applied ( -pi < arg < pi).
