## In Problems 1-8, show that f(z)dz = 0, where f is the given function and C is the unit circle |z...

COMPLEX VARIABLES

Using Cauchy-Goursay theorem solves the following:

Solve the problem (3) please

In Problems 1-8, show that f(z)dz = 0, where f is the given function and C is the unit circle |z| = 1. f(z) = z^3 - 1 + 3i f(z) = z^2 + 1/z -4 f(z) = z/2z + 3 f(z) = z-3/z^2 + 2z + 2 f(z_ = sin z/(z^2 - 25)(z^2 + 9) f(z) = e^z/2z^2 + 11z + 15 f(z) = tan z f(z) = z^2 -9/cosh z Evaluate 1/z dz, where C is the contour shown in FIGURE 5.3.9. Evaluate 5/z + 1 + i dz, where C is the contour shown in FIGURE 5.3.10.

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Sharjeel Khan
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