# Zeros, Poles, and Essential Singularities

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Let be a complex-valued function. Assign a color to each point of the complex plane as a function of , namely the RGB color with four arguments , , , and (red, green, blue, and opacity, all depending on ). If (with chosen by its slider), use black. Otherwise: if , ; if , ; if , .

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Contributed by: Izidor Hafner (February 2016)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Reference

[1] A. Sveshnikov and A. Tikhonov, *The Theory of Functions of a Complex Variable *(G. Yankovsky, trans.), Moscow: Mir Publishers, 1971.

## Permanent Citation

"Zeros, Poles, and Essential Singularities"

http://demonstrations.wolfram.com/ZerosPolesAndEssentialSingularities/

Wolfram Demonstrations Project

Published: February 26 2016