Notes

Field Axioms for Complex Numbers
The Triangle Inequality in the Complex Plane
An Example from Euclidean Geometry
DeMoivre's Theorem
The Extended Complex Plane
Limits in the Euclidean Plane and the Complex Plane
Zero Partials Implies u(x,y) Constant
The Binomial Theorem
Complex Differentiation
Polar Form of Cauchy-Riemann Equations
Principal Arguments of Products, Quotients, Logarithms and Powers
Identity for Product of Sines
Absolute Value of a Complex Integral
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

July 29, 2017