#### 1.1 Complex Arithmetic

We perform arithmetic operations on complex numbers.

#### 1.2 The Complex Plane

We learn a geometric interpretation of complex numbers.

#### 1.3 Complex Conjugate

We learn properties of the complex conjugate.

#### 1.4 The Complex Variable, z

We learn to use a complex variable.

#### 1.5 Operations in the Complex Plane

We visualize operations on complex numbers in the complex plane.

#### 1.6 Special Sets

We learn to recognize and sketch special sets in the complex plane.

#### 1.7 Hyperbolic Functions

We learn the basic properties of the hyperbolic functions.

#### 2.1 Complex Functions

We introduce functions of a complex variable.

#### 2.2 Complex Logarithms

We define and discuss complex logarithms.

#### 2.3 Complex Trigonometric Functions

We define and discuss the complex trigonometric functions.

#### 2.4 Complex Mappings

We determine the image of special sets.

#### 3.1 Complex Limits

We find limits of complex functions.

#### 3.2 Complex Derivatives

We find derivatives of complex functions

#### 3.3 Cauchy-Riemann Equations

We derive the Cauchy-Riemann equations.

#### 3.4 Analytic Functions

We determine if a function is analytic using the Cauchy-Riemann equations.

#### 3.5 Harmonic Functions

We determine and create harmonic functions.

#### 4.1 Complex Sequences

We find limits of complex sequences.

#### 4.2 Complex Series

We determine convergence of complex series.

#### 4.3 Power Series

We determine radius of convergence of complex power series.

#### 4.4 Taylor Series

We determine the Taylor series for a given analytic function.

#### 4.5 Laurent Series

We determine the Laurent series for a given function.

#### 5.1 Contour Integrals

We compute integrals of complex functions along contours.

#### 5.2 Cauchy’s Theorem

We compute integrals of complex functions around closed curves.

#### 5.3 Residue Theorem

We use the Residue Theorem to compute integrals of complex functions around closed contours.