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Complex conjugate a function

  1. Apr 29, 2013 #1
    1. The problem statement, all variables and given/known data
    Hi

    I have a complex function of the form
    [tex]
    \frac{1}{1-Ae^{i(a+b)}}
    [/tex]
    I want to take the complex conjugate of this: The parameters a and b are complex functions themselves, but A is real. Am I allowed to simply say
    [tex]
    \frac{1}{1-Ae^{-i(a^*+b^*)}}
    [/tex]
    where * denotes the c.c.? I seem to vaguely remember that [itex]f^*(x) = f(x^*)[/itex].
     
  2. jcsd
  3. Apr 29, 2013 #2
    Be careful; the rule [itex]f(z^*)=f(z)^*[/itex] doesn't in general work when [itex]z[/itex] is a complex number.
    Consider the following counterexample: take [itex]f(z)=i|z|[/itex], where [itex]|\cdot |[/itex] is the absolute value. Then [itex]f(z^*)=i|z^*|=i|z|=f(z)[/itex] but [itex]f(z)^*=(i|z|)^*=-i|z|=-f(z)[/itex], so we have [itex]f(z^*)\neq f(z)^*[/itex].

    In general, your function [itex]f[/itex] can be very nice (the example above isn't complex-differentiable) but still fail to have this property.

    For your problem, it's going to depend a lot on what your functions [itex]a,b[/itex] are.
     
  4. Apr 29, 2013 #3
    Thanks for helping out. If a and b are just complex numbers, then it should be correct, no?
     
  5. Apr 29, 2013 #4
    Yes, if a and b are just complex numbers, then it works out like that.
     
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