How Do You Prove DeMoivre's Theorem for Complex Numbers?

lostNfound
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I think I got it
 
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Start by writing (1+i)n in trigonometric form.

What theorem do you have about raising a complex number in trigonometric form to the nth power?
 
I think I got it
 
Last edited:
LCKurtz said:
Start by writing (1+i)n in trigonometric form.

What theorem do you have about raising a complex number in trigonometric form to the nth power?

lostNfound said:
I did try putting (1+i)^n in trigonometric form and I got the following:
2^(n/2)*(cos(45*n)+i*sin(45*n))

OK. Now what about the answer to my question? What theorem do you have...? Look in your book.
 
DeMoivre' Thm
 
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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