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

Hi,

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