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Calculus IV
15.Functions of Several Variables
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Course: Trigonometry
Topic: Complex, Parametric, and Polar Forms
Subtopic: Powers and Roots in Trig Form

Overview

From an intermediate algebra course we know how to expand and simplify a Complex number in the form (a+bi)n via multiple FOILs or using Pascal's Triangle. In this lesson we convert the Complex number to trig form and use a formula to evaluate (r·cisθ)n which is a great time saver!

We also learn something we never learned to do in intermediate algebra, that is to take roots of Complex numbers in trig form nth-root((r·cisθ)=(r·cisθ)1/n. Finding powers and roots of Complex numbers in trigonometric form use one of two formulas called DeMoivre's Theorems.

Objectives

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

Terminology

Define: DeMoivre's Theorem of Powers, DeMoivre's Theorem of Roots