complex analysis 6

any help would be great!
it is the link below

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So, what did you try?

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?

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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Originally Posted by shaheen7

Does this show that the integral has a finite limit?

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No, but the fact that decays faster than any polynomial, for any does. For the last one use Green's theorem, Fubini and the representation of you got.

i'm a bit confused as to how you got e^-ct. did you get that by integrating the function?