The Fundamental Theorem of Algebra says that all nonconstant polynomials have roots in the complex numbers. You might have heard this before, but if you are like me then a proof of this theorem was withheld from you for a few years. Your wait is over. In this talk we will discuss some basic facts about calculus of functions of a complex variable, and then use them to prove the Fundamental Theorem of Algebra.

Prerequisites for this talk are familiarity with the arithmetic of complex numbers (addition and multiplication, absolute value and polar form), and traditional calculus of two variables (namely Green's theorem).

USG funded