**Intended Audience**: Undergraduates, advanced high-schoolers and high-school teachers interested in showing their students some advanced mathematics.

In this episode we introduce the complex derivative and discuss some of its properties.

Deceptively similar in its definition to the usual derivative of a real valued function (of one variable), the complex derivative is a truly profound mathematical concept. This video defines the complex derivative and proves that a function is complex differentiable if and only if it satisfies the so-called Cauchy-Riemann equation.

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©2016 David Shea Vela-Vick