With this tool you can visualize complex-valued functions by assigning a color to each point in the complex plane according to its argument/phase. The identity function f(z)=z shows how colors are assigned.

Input box:
Enter any expression in z. Here are some example functions to try:

• (z^2+i)/(iz-1)^2
• sin(z)+e^(cos(z))
• log(z)-sech(z+i)
• 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: prod(e^((z+(e^(2*pi*i/5))^n )/(z-(e^(2*pi*i/5))^n)), 5)
• Iterated function: iter(z+z'^2,z,15)

---

Menu ☰

Level curves: Select an option to draw level curves. Depending on the color scheme you will have different options: 'Phase', 'Modulus', 'Phase/Modulus', 'Real', 'Imaginary', 'Re/Im', 'Standard' or 'None'.

Parameters: You can also use three parameters in your function, e. g.

• z + t, where 0 ≤ t ≤ 1,
• exp(u * z), where u = exp(i*s) and 0 ≤ s ≤ 2pi
• z^n, with 0 ≤ n ≤ 30

Use the sliders to change these parameters.

Zoom In/Out Press or to zoom in or out. Alternatively use the mouse wheel. You can also change the view by dragging the plot.

That's it! If you found this tool useful, I would appreciate your support in