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Visualizing Complex Functions
A blog for my thoughts. Mostly philosophy, math, and programming.
\[z = x + yi\] While the axes directly correspond to each component, it is actually often times easier to think of a complex number as a magnitude (\(r\)) and angle (\(\theta\)) from the origin. A branch cut means that the function surface gets too complicated to represent in two dimensions, so it is truncated along the negative x-axis for simplicity. Opposing poles appear out of thin air along the imaginary axis and pull back, leaving a sequence of vertical contours on the negative real side of the function in similar manner to \(\mathrm{e}^z\).
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