# Chapter 6: Polar System

**At Grade**Created by: CK-12

## Introduction

When graphing numbers, you are accustomed to plotting points on a "rectangular coordinate system", involving "x" and "y" coordinates. However, there is another way to plot numbers, called a "polar coordinate system". This Chapter will introduce you to how to plot numbers on this coordinate system, as well as how to translate a plot from rectangular coordinates to polar coordinates, and vice versa.

After this, you'll be introduced to how to integrate your knowledge of complex numbers and their functions into this newly described method of plotting.

- 6.1.
## Plots of Polar Coordinates

- 6.2.
## Distance Between Two Polar Coordinates

- 6.3.
## Transformations of Polar Graphs

- 6.4.
## Polar to Rectangular Conversions

- 6.5.
## Rectangular to Polar Conversions

- 6.6.
## Rectangular to Polar Form for Equations

- 6.7.
## Intersections of Polar Curves

- 6.8.
## Equivalent Polar Curves

- 6.9.
## Trigonometric Form of Complex Numbers

- 6.10.
## Product Theorem

- 6.11.
## Quotient Theorem

- 6.12.
## DeMoivre's Theorem

- 6.13.
## DeMoivre's Theorem and nth Roots

- 6.14.
## Equations Using DeMoivre's Theorem

- 6.15.
## Geometry of Complex Roots

### Chapter Summary

## Summary

This Chapter presented polar plots. Included were topics about how to plot values on a polar coordinate system, as well as how to translate between rectangular and polar coordinates. This was followed by how to describe complex numbers in trigonometric form, and theorems dealing with these relationships, including the Product Theorem, the Quotient Theorem, and DeMoivre's Theorem. The Chapter concluded with sections on how to solve equations in complex numbers and the geometry of complex roots.