The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

DeMoivre's Theorem: Standard Form

Date: 3/19/96 at 18:43:13
From: Robert Holscher
Subject: Math

Dr. Math,

I have no idea how to begin to solve this problem.

Use DeMoivre's theorem to write (1-i)^10 in standard form.

Please help!

Rob Holscher

Date: 3/22/96 at 19:23:50
From: Doctor Sebastien
Subject: Re: Math


De Moivre's Theorem: (cos x + i sin x)^n = cos nx +i sin nx, 
where n is any real number.

The key to your problem is to find x such that cos x = 1 and 
sin x = -1.

When x =- Pi/4, cos x=1/SQRT(2) and sin x = -1/SQRT(2), 
where SQRT means square root.

Therefore, (1-i)^10 = {SQRT(2)*(cos (-Pi/4) + i sin (-Pi/4))}^10
= (SQRT(2)^10)*(cos (-5Pi/2) + i sin (-5Pi/2)), by DeMoivre's 
theorem =32 * -i = -32i

Doctor Sebastien, The Math Forum

Associated Topics:
College Imaginary/Complex Numbers

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.