Complex space: Areas in complex space
This graphic allows the real part, the imaginary part or the absolute value of complex functions to be displayed in three dimensions above the complex plane. This makes it easy to identify the poles or zero points of a function.
In this graph, the availability of variable names in the function editor is limited to z and param as well as x and y as representatives of the real part or the imaginary part of the variable z. Enter the desired function in the input field for the function, or select one of the existing functions by clicking on the arrow to the right of the input field. The parameter param is always assumed to be a purely real value in this graph.
The values between which the real part and the imaginary part vary can be defined as desired. They can also be opposite – the end value can be smaller than the start value. However, it should be noted that CGRAPH uses a 3D representation in which the centre point (0/0/0) is always in the centre of the representation. Areas that are far outside the zero point can therefore only be viewed from a distance or may even be outside the viewer's position.
The z-coordinate can optionally represent the real part, the imaginary part or the magnitude of the function.
CGRAPH displays the area within the range specified for the variable.
After clicking the Create graph button, CGRAPH switches to the Graphics tab and displays the graph.
The default values can be viewed in the tree on the left-hand side. Clicking on the (optional) parameter also activates the parameter's adjustability at the bottom. An explanation of this function can be found in the notes on changing the parameter in the graphic display.
Double-clicking on the text next to the coloured symbol allows you to set the colour and appearance of the graph. Clicking on the coloured symbol itself hides or shows the graph.
The default values can be changed later – clicking on one of the values switches CGRAPH back to the tab with the default values. The graphic is adjusted as soon as the Create graphic button is clicked.