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November 01, 2025, 03:15:45 pm
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Author Topic: de moivre's theorem?  (Read 921 times)  Share 

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Yoda

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de moivre's theorem?
« on: November 06, 2014, 09:48:03 pm »
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solve z^3=i    how do you do that?
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RKTR

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Re: de moivre's theorem?
« Reply #1 on: November 06, 2014, 09:57:56 pm »
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r^3 cis(3x) =cis(pi/2)
r=1  3x=pi/2+2n pi ,n is element of Z
         x=pi/6  + 2npi/3

n=0,x=pi/6
n=-1,x=-pi/2
n=1,x=5pi/6

z=cis(pi/6) ,z=cis(-pi/2) ,z=cis(5pi/6)
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Yoda

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Re: de moivre's theorem?
« Reply #2 on: November 06, 2014, 10:12:36 pm »
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how did you get cis(pi/2) in the first line?
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keltingmeith

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Re: de moivre's theorem?
« Reply #3 on: November 06, 2014, 10:18:34 pm »
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Quote from: Yoda on November 06, 2014, 10:12:36 pm
how did you get cis(pi/2) in the first line?
Because i=cis(pi/2)
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