FunctionFamilies.html

Complex Exponential Function

The function is w = exp(z). The blue grid is in the z = x+iy domain, the red 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 = e^x+iy written as w = e^x e^iy = e^x(cos(y) + i sin(y)).