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Math Help - complex analysis 6

  1. #1
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    complex analysis 6

    any help would be great!
    it is the link below

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  2. #2
    Super Member girdav's Avatar
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    So, what did you try?
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  3. #3
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    given that z = x + iy,
    modulus(e^xt*e^iyt)/modulus (t + 1). Since Re(z) < 0, e^xt --> 0. Does this show that the integral has a finite limit?
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  4. #4
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    also Morera's theorem states that f should be continuos and int(f) = 0. Does the above e^xt --> 0 show int(f) = 0, or do we have to solve the integral?
    i suppose f is not discontinuous on S?
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  5. #5
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    Quote Originally Posted by shaheen7 View Post
    Does this show that the integral has a finite limit?
    No, but the fact that e^{(-ct)} decays faster than any polynomial, for any c>0 does. For the last one use Green's theorem, Fubini and the representation of F' you got.
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  6. #6
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    i'm a bit confused as to how you got e^-ct. did you get that by integrating the function?
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