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Homework Help: The exponential identity

  1. Jan 30, 2010 #1
    1. The problem statement, all variables and given/known data
    Let z=x+iy prove that Exp[z1]*Exp[z2]=Exp[z1+z2]


    2. Relevant equations
    Binomial thm (x+y)^n=Sum[Bin[n,k]*x^n-k*y^k,{k,1,n}]


    3. The attempt at a solution
    I have no idea about this question...

    Please give me some help.
     
  2. jcsd
  3. Jan 31, 2010 #2

    HallsofIvy

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    Science Advisor

    I don't see how the binomial theorem has anything to do with this. I think better would be
    [tex]e^{a+ bi}= e^a(cos(b)+ i sin(b))[/tex]
    together with [itex]e^{x+y}= e^x e^y[/itex], cos(x+y)= cos(x)cos(y)- sin(x)sin(y), and sin(x+y)= sin(x)cos(y)+ cos(x)sin(y).
     
  4. Feb 1, 2010 #3
    The hint was given by my teacher, but I think he is a little unreliable.
     
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