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October 26th, 2013, 09:32 AM   #1
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Complex Numbers question (de Moivres)

Can anyone help me with this problem? In the attached photo, I have highlighted the area I need help with. I don't understand what happens to the ^1/4 , and how it changes the other numbers. - e.g.: why does the 2n(pi) change to pi(n)/2
I have an idea of what happens, but I would like a proper explanation and why it happens so I can know it better.
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 October 26th, 2013, 09:58 AM #2 Senior Member   Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116 Re: Complex Numbers question (de Moivres) DeMoivre's formula says that: $(sin(x) + icos(x))^n= (sin(nx) + icos(nx))$ This also works for 1/n in the sense that: $sin(\frac{x}{n}) + icos(\frac{x}{n})= \ an \ nth \ root \ of \ sin(x) + icos(x)$ So, the 1/4 has gone inside the sin and cos.
October 26th, 2013, 10:55 AM   #3
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Re: Complex Numbers question (de Moivres)

Quote:
 Originally Posted by Pero DeMoivre's formula says that: $(sin(x) + icos(x))^n= (sin(nx) + icos(nx))$ This also works for 1/n in the sense that: $sin(\frac{x}{n}) + icos(\frac{x}{n})= \ an \ nth \ root \ of \ sin(x) + icos(x)$ So, the 1/4 has gone inside the sin and cos.
Thanks I understand now, it actually says that in my book but I was getting confused by the 2nPi in general polar form

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