Math Problem Statement

Describe cauchy's fundamental theorem for evaluating complex intregal and justify the theorem for the function :

f(z) = z^3 + i(z)^2 -5z + 2i if C is the circle |z| = 1 described in the positive sense

Solution

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Math Problem Analysis

Mathematical Concepts

Complex Analysis
Contour Integration

Formulas

Cauchy's Integral Theorem: \( \oint_C f(z) \, dz = 0 \)

Theorems

Cauchy's Integral Theorem

Suitable Grade Level

Undergraduate Mathematics