Complex Surfaces 3D Object

Michael Tritle
MATH 401 3D Printing
October 29, 2019

The complex numbers are a generalization of the real numbers. Complex numbers can be written in the form x + yi where x,y are elements of the set of real numbers, and i is an imaginary number, which is sqrt(-1). Essentially, we view complex numbers as a combination of real and imaginary numbers, in that complex numbers have a real and an imaginary part. To represent real numbers visually, we consider a number line. To represent complex numbers visually, we use a plane. It's standard that the x - axis represents the real part, and the y - axis represents the imaginary component. So, the complex number 2 + 3i would be analogous to the point (2, 3) on the usual Cartesian Plane.

If we were are to a consider a function of a single real variable, we see that any input from the functions domain maps to a single real valued output. Functions of a complex variable are the same in that any complex input from the functions domain maps t