×

**Phase Portraits of Complex Functions**

This tool visualizes complex-valued functions by assigning a color (HSB scheme with a gradient method) to each point in the complex plane according to its argument/phase. The identity function f(z)=z shows how colors are assigned.

f(z): Enter any expression in z. Here are some example functions to try

- z^2
- z^3-1
- 1/z^5
- (z+1)/(z-1)
- sin(z)
- e^z
- log(z)
- sech(z)
- arctan(z)
- (z-1)(conj(z)^2+conj(z)+1)
- 0.926(z
+7.3857e-2 z^5 +4.5458e-3 z^9) - Jacobi Elliptic: sn(z, 0.3)
- Gamma function: gamma(z)
- Taylor Series: sum((-1)^n*z^(2n)/(2n)!, 7)
- Atomic Singular Inner Function: multIter(e^((z+(e^(2*pi*i/5))^n )/(z-(e^(2*pi*i/5))^n)), 5)
- Iterated function: iter(z+z'^2,z,15)

|Re z|<: Drag or enter a positive number to define the domain (square/rectangle) for plotting the function.

Save (png): Click to save your plot.

That's it! If you found this tool useful, or an issue, please let me know: j.ponce@uq.edu.au