Complex Exponential Function
The function is w = exp(z). The red grid is in the
z = x+iy domain, the blue image is in the
w = u+iv domain.
Along lines parallel to the real axis, exp behaves like its real counterpart.
However, along paths parallel to the imaginary axis, exp is shown to be
a periodic function. This result is initially surprising, but becomes obvious considering
w = ex+iy written as
w = ex eiy
= ex(cos(y) + i sin(y)).