# complex analysis 6

• May 7th 2011, 12:39 PM
shaheen7
complex analysis 6
any help would be great!

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• May 7th 2011, 12:55 PM
girdav
So, what did you try?
• May 7th 2011, 02:12 PM
shaheen7
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?
• May 7th 2011, 02:16 PM
shaheen7
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?
• May 7th 2011, 11:13 PM
Jose27
Quote:

Originally Posted by shaheen7
Does this show that the integral has a finite limit?

No, but the fact that \$\displaystyle e^{(-ct)}\$ decays faster than any polynomial, for any \$\displaystyle c>0\$ does. For the last one use Green's theorem, Fubini and the representation of \$\displaystyle F'\$ you got.
• May 9th 2011, 08:13 PM
shaheen7
i'm a bit confused as to how you got e^-ct. did you get that by integrating the function?