Perplex numbers are a kind of alternative to complex numbers. They are numbers of the form x + j y, where j is not a real number, but satisfies j2 = 1. Like the complex numbers C, the perplex numbers P are in one-to-one correspondence with the points in the xy-plane with x + j y corresponding to the point (x, y). We will see how P differs from C, use Mathematica to explore some of the elementary functions on P, and see what holomorphic functions are like in this setting. A familiarity with the complex plane and complex functions will be helpful to audience members.