24 Views of the Complex Exponential Function

y = ex x = Re(eiy) = cos y x = Im(eiy) = sin y
Color map Discrete color map Color coded surface
Re(ex+iy) Im(ex+iy) |ex+iy|
In Four Dimensions
Conformal maps


If you have installed the free viewer, clicking on an image above will open a corresponding document.

In the color maps, hue indicates phase, saturation and lightness indicate magnitude. Real values are cyan, pure imaginary values are red. In general, one can see the sinusoidal variation along the imaginary or y-axis and exponential variation along the real or x-axis.


  1. 24 ways of looking at Dao De Ching 33
  2. 24 Views of Mt. Fuji by Hokusai Katsushika
  3. The Complex Exponential and Complex Logarithm
  4. Exponential Tetraview
  5. Visualizing Functions of a Complex Variable
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