Precalculus

8.

Polar Coordinates and Complex Numbers

8.1.

Polar Coordinate System

8.1.1.

Definition of Polar Coordinates

8.1.2.

Plotting Points in Polar Coordinates

8.1.3.

Multiple Representations of Points

8.1.3.1.

Adding 2π to Angle

8.1.3.2.

Negative Radius

8.1.4.

Converting Between Polar and Rectangular Coordinates

8.1.4.1.

Polar to Rectangular

8.1.4.2.

Rectangular to Polar

8.2.

Graphs of Polar Equations

8.2.1.

Basic Polar Graphs

8.2.1.1.

8.2.1.2.

Lines Through Origin

8.2.1.3.

Horizontal and Vertical Lines

8.2.2.

8.2.2.1.

Even and Odd Petals

8.2.2.2.

Equations of Rose Curves

8.2.3.

8.2.3.1.

With and Without Inner Loops

8.2.3.2.

8.2.4.

8.2.5.

Spiral of Archimedes

8.2.6.

Converting Between Polar and Rectangular Equations

8.2.7.

Symmetry in Polar Graphs

8.2.7.1.

Symmetry about Polar Axis

8.2.7.2.

Symmetry about Line θ = π/2

8.2.7.3.

Symmetry about Pole

8.3.

Complex Numbers in Polar Form

8.3.1.

Graphing Complex Numbers

8.3.1.1.

8.3.1.2.

Real and Imaginary Axes

8.3.2.

Absolute Value of Complex Numbers

8.3.2.1.

Modulus or Magnitude

8.3.2.2.

Distance from Origin

8.3.3.

Argument of Complex Numbers

8.3.3.1.

Principal Argument

8.3.3.2.

General Argument

8.3.4.

Polar Form of Complex Numbers

8.3.4.1.

r(cos θ + i sin θ)

8.3.4.2.

Converting from Rectangular to Polar

8.3.4.3.

Converting from Polar to Rectangular

8.3.5.

Multiplication in Polar Form

8.3.6.

Division in Polar Form

8.3.7.

DeMoivre's Theorem

8.3.7.1.

Powers of Complex Numbers

8.3.8.

Roots of Complex Numbers

8.3.8.1.

8.3.8.2.

8.4.

Parametric Equations

8.4.1.

Introduction to Parametric Equations

8.4.1.1.

8.4.1.2.

Parametric Curves

8.4.2.

Graphing Parametric Equations

8.4.2.1.

Creating Table of Values

8.4.2.2.

Plotting Points

8.4.2.3.

Indicating Direction

8.4.3.

Eliminating the Parameter

8.4.3.1.

Algebraic Methods

8.4.3.2.

Trigonometric Methods

8.4.4.

Finding Parametric Equations

8.4.4.1.

From Rectangular Equations

8.4.4.2.

From Geometric Descriptions

8.4.5.

Applications of Parametric Equations

8.4.5.1.

Projectile Motion

8.4.5.2.

8.4.5.3.

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