Notes

Field Axioms for Complex Numbers

The Extended Complex Plane

An Example from Euclidean Geometry

Limits in the Euclidean Plane and the Complex Plane

Complex Differentiation

The Binomial Theorem

Identity for Product of Sines

Principal Arguments of Products, Quotients, Logarithms and Powers

Absolute Value of a Complex Integral

Examples Involving Branch Cuts

Differentiation and Integration of Power Series

The Exponential Function as a Limit

The Binomial Series

Manipulating Power Series

Lacunary Series

Jordan's Lemma

Evaluating Dirichlet's Integral

Techniques for Finding Residues