The Complex Sine Function
by Steven J. Wilson

By varying the parameters, you can use this page to study the behavior and zeros of the complex sine function whose equation is:

f(z) = b₁ sin(a₁z + a₂) + b₂

Note: Due to both algorithmic and resolution issues, some of the graphs may not be completely perfect.

Parameter Input: (for imaginary values, use a capital "I")
a₁:
a₂:
b₁:
b₂:

These graphs are 2D slices (along the real and/or imaginary axes) of the 4D graph of the complex sine function.

These graphs are 3D slices of the 4D graph of the complex sine function. The graph on the left shows the real parts of the function, and the graph on the right shows the imaginary parts.

These are level curves of the two 3D graphs above. The level curve at height zero is given in red.

In this graph, we superimpose the level curves at height zero from both of the contour graphs above. The red curves give the zero curves for the real part, and the blue curves give the zero curves for the imaginary part. Each intersection of a red and a blue curve is a zero of the complex sine function.