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

Sorry, the applet is not supported for small
screens. Rotate your device to landscape. Or resize your window so it's
more wide than tall.

Top

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

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

Sorry, the applet is not supported for small
screens. Rotate your device to landscape. Or resize your window so
it's more wide than tall.

Top

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

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

Sorry, the applet is not supported for small
screens. Rotate your device to landscape. Or resize your window so
it's more wide than tall.

Top

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

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

Sorry, the applet is not supported for small
screens. Rotate your device to landscape. Or resize your window
so it's more wide than tall.

Top

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

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

Sorry, the applet is not supported for small
screens. Rotate your device to landscape. Or resize your window
so it's more wide than tall.

Top

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-