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#1 2007-09-05 13:16:09

teo
Member
Registered: 2007-08-04
Posts: 7

complex numbers

Using De Moivre's theorem, express (1-i)^-7 in x+yi form


to take the first step is easy, to climb up the mountain is another matter.

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#2 2007-09-05 15:42:57

bossk171
Member
Registered: 2007-07-16
Posts: 305

Re: complex numbers

Well, I've learned something today, I've never heard of De Moivre's theorem but a few minutes over at wikipedia gave me a clue as to what it is, but I'm having a little trouble applying it. Instead, let's do it the old fashion way:

In step one, I use an exponent rule:

Then I uber-FOILed (made up word there) using pascal's triangle and some basic imaginary rules (actually, I had google do the work, but I can do it here:

I then rationalized it by multiplying the numerator and denominator by the conjugate of 8 + 8i (which is 8-i).

Well, that was fun and time consuming, but it still doesn't really give you what you were looking for.


There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

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#3 2007-09-05 16:21:40

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

Re: complex numbers

The Complex Number Calculator gets 0.0625-0.0625i, so it agrees with you!

But still no De Moivre


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#4 2007-09-05 20:47:55

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: complex numbers

Isn’t it obvious that

Tsk tsk, all of you! shame

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#5 2007-09-06 10:26:02

mamoo
Member
Registered: 2007-09-06
Posts: 3

Re: complex numbers

where     
    and 

and by De Moivre Theorem

now consider 1 -i =

since cos(-x) = cos x 

now with De Moivre Theorem
(1-i)^7 =

           =

       
                                   
           =
since cos(-x) = cos x

           =

since sin(7pi/4) = -sqrt(2)/2

           =

           =

           =

since (1/sqrt(2)^6) = (1/8)

           =

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#6 2007-09-06 12:01:11

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

Re: complex numbers

QED!


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#7 2007-09-15 05:24:49

mamoo
Member
Registered: 2007-09-06
Posts: 3

Re: complex numbers

wat does QED means?

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#8 2007-09-15 06:17:27

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: complex numbers

Quod erat demonstrandum, a latin term meaning "What was required to be proven has been proved".

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#9 2007-09-15 07:05:38

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: complex numbers

While the interpretation is correct, I prefer the literal translation:

quod: Which
erat: was to be
demonstrandum: demonstrated


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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