Subject:
Mathematics, Calculus, Trigonometry
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Complex Numbers, DeMoivre's Theorem, Euler's Notation, Magnitude, Mathematics, Polar Coordinates, Powers and Roots of Complex Numbers, Product and Quotient of Complext Numbers, Sine-cosine Representation, Tmm0022
License:
Creative Commons Attribution-NonCommercial 4.0
Language:
English
Media Formats:
Downloadable docs, Text/HTML, Video

Education Standards (1)

Polar Form of Complex Numbers, Euler's Notation, DeMoivre's Theorem, Applications

Module Overview

Complex numbers, Euler's notation, sine-cosine representation, DeMoivre's Theorem, product and quotient of complext numbers, powers and roots of complex numbers, magnitude, polar coordinates,

Section 1: Complex Numbers and their Polar Form

In this module, complex numbers are represented in terms of polar coordinates. This representation helps in evaluating complex number arithmetic, particularly their powers and roots as an application of DeMoivre's Theorem.

Learning Objectives:

  • Complex number - real and imaginary part
  • Complex Plane
  • Modulus and Argument of a complex number, and their properties
  • Polar form of complex number
  • Euler's Formula for a complex number
  • Products, Powers and Quotients of complex numbers, DeMoivre's Theorem
  • nth roots of complex numbers