Argand

This is a Windows application for visualising complex functions.

It is named after the Argand diagram, upon which complex numbers can be plotted as points, with their real parts along the x axis and imaginary parts on the y axis.

Argand can be used in two main modes :

To display the real and imaginary parts of a complex function. One window shows the real part, as a vertical distance above the z plane. Another window shows the imaginary part above the z plane.

Alternatively it can show a transformation. One window shows a shape (rectangle, line, ellipse, grids) in the z plane, while the other shows the transformation of those points by the function onto the w plane ( where w = f(z) ). The integral of the function over the path is also shown. These conformal transformations are heavily used in physics and engineering.

Requirements : it works on versions of Windows with OpenGL, which all recent versions have built-in.

This package is free

Obtaining Argand

The download is here. Choose the save option. Once you've got it, unzip it into a suitable directory - it does not matter where, but c:/argand would be good. You will get argand.exe, together with a documentation folder. Create a short-cut to argand.exe on your desktop.

The installation is completely safe and it will not touch any dlls or the system registry.

Screenshots

Click on the thumbnail for a full-size version

This shows the real (left window) and imaginary parts of the function
w = sin( z )

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This is sin(z) again, but the right hand window is displaying a slice through the real part, here along the x axis, so we can see the familiar sine curve

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This shows a conformal transformation, of w = z*z, from a quarter circle of radius 3 to the half-plane circle radius 9

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This is the transformation of a square grid by sin( z ). Vertical lines are transformed into hyperbolae, while horizontal lines turn into circles.