Complex Function Grapher

Studio College Algebra Home, Studio Assignment, Extra Credit Assignment

Complex Function Grapher

Mathlet Instructions

Graphing a complex function is difficult because you need 2 (real) dimensions for the domain and 2 (real) dimensions for the range - a total of 4 dimensions. In this applet, the domain of a complex function is graphed on the base plane. The range is graphed using polar coordinates. The modulus (magnitude) of the complex function is graphed on the vertical axis. The argument (angle) is graphed by using different colors - light blue for positive real, dark blue (shading to purple) for positive imaginary, red for negative real, and yellow-green for negative imaginary, as shown on the right This allows four dimensions to be represented in three spatial dimensions, which are then projected onto a two dimensional screen using a simple orthogonal projection.

Enter complex functions into the f(z) = text box using standard calculator notation, then click on the view you wish to see (you may just press the Enter key if you don't want to change the view). You will need to use z for the variable (not x). You may use implied multiplication (i.e. you don't need to use a * for multiplication in (2z-1)(z^2-2)) except you must use a * for multiplication between two different alphabetic entries (e.g. you must write e^(pi*z) not e^(piz), which would leave the computer wondering what "piz" means). Functions must have parentheses, i.e. ln(z) not ln z. The parser understands the following operations, functions, and constants: +, -, *, /, ^, e, pi, i, sqrt(), exp(), ln(), log() (which is synonymous with ln, NOT common log, in keeping with practice in programming and advanced math courses), and also (functions from more advanced course) , cos(), tan(),sinh(), cosh(), abs(), mod() (synonymous with abs), arg(), and conj().

To adjust the domain of the graph, right-click (or shift-click if you have a one-button mouse) on the graph. The domain editor only accepts numerical input, i.e. 3.14 not pi.