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Math Help - analytic, harmonic, Cauchy-Riemann...

  1. #1
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    analytic, harmonic, Cauchy-Riemann...

    a. Let f(z) = z + 1/z. Determine all points at which f(z) is analytic. Use the Cauchy-Riemann equations to determine f'(z).

    b. Let v = (x^2 - y^2)^2. Determine if v is harmonic. If your answer is yes, find a corresponding analytic function f(z) = u(x,y) + iv(x,y).

    c. Let f(z) = e^(-x)e^(-iy). Show that f(z) is analytic everywhere and determine its derivative.


    Please help!! And if you could show the steps so I could follow what you are doing, I would really appreciate it.
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  2. #2
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    Quote Originally Posted by SoBeautiful View Post
    a. Let f(z) = z + 1/z. Determine all points at which f(z) is analytic. Use the Cauchy-Riemann equations to determine f'(z).
    Here.
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  3. #3
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    Quote Originally Posted by SoBeautiful View Post

    b. Let v = (x^2 - y^2)^2. Determine if v is harmonic. If your answer is yes, find a corresponding analytic function f(z) = u(x,y) + iv(x,y).
    For some reason I think I made a mistake.
    This is Mine 57th Post!!!
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  4. #4
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    Most importantly about #2, the function v(xy) is not harmonic.
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  5. #5
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    What is the E in part b? And doesnt u(x,y) = 0?
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  6. #6
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    Quote Originally Posted by SoBeautiful View Post
    What is the E in part b? And doesnt u(x,y) = 0?
    You are kidding. Are you not?
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