CN - Complex Numbers Module Overview

Complex Numbers Module Overview

Introduction

In previous courses, you've learned about complex numbers as the imaginary solutions to quadratic or polynomial functions. In the field of Physics, complex numbers are used in electronic and electromagnetism engineering and quantum mechanics. Mathematicians use complex numbers to solve differential equations and apply it in many analysis fields. In this module, we will study the graphical representation of complex numbers in both rectangular and polar form. But, we will begin with a review of operations with complex numbers.

Essential Questions

How can I represent complex numbers graphically?
How does the complex plane show addition, subtraction, and conjugation of complex numbers?
What are two ways to represent complex numbers?
When given two points on the complex plane, what does it mean to find the distance between them and the midpoint of the segment connecting them?

Complex Numbers Key Terms

The following key terms will help you understand the content in this module.

Complex Numbers - A class of numbers including purely real numbers a, purely imaginary number bi, & numbers with both real and imaginary parts a + bi

Rectangular form of a complex number - a + bi

cisθ - Shorthand for equation image indicator $LaTeX: \cos\theta+i\sin\theta$ $\cos\theta+i\sin\theta$

Polar Form of a Complex Number - equation image indicator $LaTeX: r\left(\cos\theta+i\sin\theta\right)=r\left(cis\theta\right)$ $r\left(\cos\theta+i\sin\theta\right)=r\left(cis\theta\right)$

Complex Conjugate of z = a + bi - $LaTeX: \overline{z}=a+bi$ $\overline{z}=a+bi$

Modulus of a Complex Number - the distance between a number and 0 when plotted on the complex plane. equation image indicator $LaTeX: \left|z\right|=\left|a+bi\right|=\sqrt[]{a^2+b^2}$ $\left|z\right|=\left|a+bi\right|=\sqrt[]{a^2+b^2}$ . The modulus is also referred to as the absolute value.

IMAGES CREATED BY GAVS