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Proof of complex number identity

  1. Jul 15, 2010 #1
    1. The problem statement, all variables and given/known data

    Attached question

    2. Relevant equations



    3. The attempt at a solution

    The second part of question is relatively easy, it is the first part of the question where I need help with(using arg zw = arg z + arg w to show arg z^n = n arg z).

    Also, is the question asking to proof de Moivre's formula with the identity arg zw = arg z + arg w? or just proof LHS=RHS?
     

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  3. Jul 15, 2010 #2

    alxm

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    I guess it's the induction that's causing problems. Show that it's true for z2. Then show that if it's true for zn, that it's also true for zn+1.

    The second part uses the relation you proved in the first part.
     
  4. Jul 16, 2010 #3

    eumyang

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    The base case would be for z1, I thought. In any event, it's easy to prove.
    The inductive case: assume true for n = k, show that it's true for n = k + 1.
    Here's a hint: xa + 1= (xa)(x).


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