In this plot, a grid is drawn marking certain points \(x+yi\) with a color (left).
Then that point is transformed, so that \(f(x+yi)\) is plotted with the same color as the original \(x+yi\) that it came from (right).
\(r=|z|\) circles are colored grey with intensity based on their distance from zero (from black → white as \(r\) goes from \(0\to\infty\)), with r=1 plotted black to make it stand out.
\(\theta=\arg(z)\) lines are plotted as hue (from red → orange → yellow → green → cyan → blue → magenta → red as \(\theta\) goes from \(0\to2\pi\)).
\(x+yi\) points in the domain might be mapped to the same points in the range. These may be plotted on top of each other, and some information lost.
In better but more inaccurate cases, rounding error causes the points to be plotted next to each other, so both are visible.
Enter your function here:
\(f(z)= \) →
\(r \in\) [0,]