z → tanh(z/2) = sinh(z/2)/cosh(z/2) = (exp(z) - 1)/(exp(z) + 1)
-1.7 ≦ Re(z) ≦ 1.7, -pi ≦ Im(z) ≦ pi.
i*tan(z) = tanh(i*z)
z → w = exp(z) → (w - 1)/(w + 1)
w → (w - 1)/(w + 1)
z_hyperbolic_tangent.pdf