# Math Help - complex analysis 6

1. ## complex analysis 6

any help would be great!

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2. So, what did you try?

3. 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?

4. 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?

5. Originally Posted by shaheen7
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.

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