## Examples

The following are some examples of multiple-valued functions. In each case, the branch is identified with a diferent 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.

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