Graphing a Complex Function
Instructions
Enter complex functions into the f(z) = text box using standard calculator
notation. Note that complex functions are usually written as functions
of z, and the applet requires you enter the function in terms of a
variable z. You can use implied multiplication such as 2z without a *. If
you use implied multiplication between two alphabetic entities, e.g.
zsin(piz), the system does pretty well at recognizing you meant
z*sin(pi*z). You can help make sure the system interprets things
correctly by using spaces, e.g.
z sin(pi z), or entering an explicit mulitplication sign *.
Functions
must have parentheses, i.e. sin(z) not sin z. The parser understands the
following operations, functions, and constants: +, -, *, /, ^,
sqrt(),
sin(), cos(), tan(), exp(), ln(), log() (synonymous with ln),
sinh(), cosh(), abs(), mod() (synonymous with abs), arg(), conj(), e, pi,
i.
The app shows the graph of the complex function with the domain plotted
along the base plane, the modulus of the range plotted along the z-axis,
and the argument indicated by the color according to the color wheel drawn
below. This represents the 4-dimensional complex graph as a colored
3-dimension graph. If you select the Side View the 3d graph is plotted on
the 2d screen using a standard projection. If you choose the Top View you
will only be shown the color for each point and not the height in a 2d
plot.
