Complex Derivative Field
There is a direct analogy relating the real and imaginary components of the complex derivative to divergence and curl (respectively) of a 2D vector field.
Let be a complex-differentiable complex function and
be the corresponding 2D vector field:
Complex Number Surface | Vector Field |
---|---|
So
(note) Here curl is a scalar, referring to the component orthogonal to the x-y plane, which is the only non-zero component in the 2D case.
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