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Calculus III

Course: Trigonometry
Topic: Complex, Parametric, and Polar Forms
Subtopic: Trigonometric Form of Complex Numbers

Overview

In an intermediate algebra course you wrote Complex numbers in standard (a+bi) form. But this is not the only way to express them. Engineers typically use the Trigonometric Form of a Complex Number instead. Our goal today is to learn to write complex numbers in trigonometric form, plot them on a Complex plane, and convert them between standard and trig form.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 9.1.1 Understand the Complex plane geometrically and algebraically
• 9.1.2 Plot Complex numbers on the Complex plane
• 9.1.3 Convert a Complex number from standard form to trigonometric form
• 9.1.4 Convert a Complex number from trigonometric form to standard form
• 9.1 5 Know the geometric connection between a complex number and its opposite, and between a complex number and its conjugate
• 9.1.6 Perform operations with Complex numbers electronically

Terminology

Terms you should be able to define: Complex plane, modulus / opposite / conjugate / argument (all of a Complex number), trigonometric form, the acronym "cis"

Supplementary Resources

Performing operations with complex numbers manually is not difficult, but if you want to do so electronically I have directions for Texas Instruments calculators TI-84, TI-86, and TI-89 here: Prof. Keely's Calculator Guide: Complex Numbers.