Examples
The following are some examples of multiple-valued functions. In each case, the branch is identified with a
different color. Click on the following functions or scroll down to explore.

\(f(z) = z^{1/2}\) \(f(z) =
z^{1/3}\) \(f(z) = \sqrt{1-z^2}\) \(f(z) = \dfrac{1}{\sqrt{1-z^2}}\) \(f(z) = \arctan(z)\)

Real component of \(f(z)=z^{1/2}\)

Imaginary component of \(f(z)=z^{1/2}\)

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Real component of $f(z)=z^{1/3}$

Imaginary component of $f(z)=z^{1/3}$

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Real component of \(f(z)=\sqrt{1-z^2}\)

Imaginary component of \(f(z)=\sqrt{1-z^2}\)

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Real component of \(f(z)=\frac{1}{\sqrt{1-z^2}}\)

Imaginary component of \(f(z)=\frac{1}{\sqrt{1-z^2}}\)

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Real component of \(f(z)=\arctan(z)\)

Imaginary component of \(f(z)=\arctan(z)\)

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Note: All applets made with MathCell created by Paul Masson .
The source code is available here.

NEXT: Mappings

[ intro , source , issues ]

ISBN: 978-0-6485736-0-9
© Juan Carlos Ponce Campuzano 2019-