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Complex numbers and induction

  • Thread starter mikee
  • Start date
  • #1
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Homework Statement

If z is a non-real complex number such that z+1/z=2costheta, prove that z^n+1/z^n=2cosntheta for any posistive integer n



Homework Equations


I think the process of induction would work, but im not quite sure how to do that with all of the unknowns, would i just treat costheta as a constant number


The Attempt at a Solution

 

Answers and Replies

  • #2
olgranpappy
Homework Helper
1,271
3

Homework Statement

If z is a non-real complex number such that z+1/z=2costheta, prove that z^n+1/z^n=2cosntheta for any posistive integer n



Homework Equations


I think the process of induction would work, but im not quite sure how to do that with all of the unknowns, would i just treat costheta as a constant number


The Attempt at a Solution

Apparently
[tex]
z=e^{i\theta}
[/tex]
...does that help?
 
  • #3
rock.freak667
Homework Helper
6,230
31
If z=cosx+isinx, what is z^n?
 

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