Module 8: Polar Coordinates & Complex Numbers
Explore the polar coordinate system, convert between systems, graph polar equations, and use DeMoivre's Theorem.
Learning Objectives
- Plot points in polar coordinates and understand multiple representations
- Convert between polar and rectangular coordinates and equations
- Graph classic polar curves (circles, cardioids, roses, lemniscates)
- Write complex numbers in trig form and apply DeMoivre's Theorem
Module Lessons
1
The Polar Coordinate System
Understand polar coordinates (r, θ), plot points, and find multiple representations.
2
Converting Between Polar and Rectangular
Convert points and equations between rectangular and polar form.
3
Graphing Polar Equations
Graph circles, cardioids, limacons, rose curves, and lemniscates.
4
Complex Numbers in Trig Form and DeMoivre's Theorem
Write complex numbers as r(cosθ + i sinθ) and find powers and roots.