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

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Homework Help Overview

The discussion revolves around proving DeMoivre's Theorem for complex numbers, specifically using the expression (1+i)^n and its representation in trigonometric form.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants suggest starting with the trigonometric form of (1+i)^n and inquire about the relevant theorem for raising complex numbers in this form to the nth power.

Discussion Status

Some participants have attempted to express (1+i)^n in trigonometric form and have shared their findings. There is an ongoing inquiry into the theorem applicable to this situation, with references made to looking up information in textbooks.

Contextual Notes

There appears to be a focus on understanding the relationship between complex numbers in trigonometric form and DeMoivre's Theorem, with some participants expressing uncertainty about the theorem itself.

lostNfound
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I think I got it
 
Last edited:
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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
 
Last edited:

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