1. (30 pts) Evaluate the given integral, where $C$ is the circle with positive orientation: \\ $\int_C \frac{e^{2022z}}{z^4 + 2z^3 + 5z^2} dz$, $C: |z + 1 + 2i| = 3$. \\ In addition, plot the region and holes to support your calculations.
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The formula states that if f(z) is analytic inside and on a simple closed curve C, and a is any point inside C, then the value of the integral of f(z) around C is given by: ∮C f(z) dz = 2πi * f(a) In this case, the given integral is: ∮C e^z dz To use the Show more…
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