Complex numbers in dilations?

Question

What happens when you include a complex number in a dilation in geometry?

Answer 1

Each complex number z can be written as re^iθ, where r=|z| and θ is the argument (typically between -π and π). The factor of r acts as a dilation, stretching or shrinking the graph, while e^iθ rotates the graph through an angle θ about the origin.