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 CauchyRiemann 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