Math Problem Statement
Apply the Cauchy integral formula appropriately to compute in counter clockwise direc- tion
i. Z sin(4z)dz C[0,2] 4z−π2
Solution
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Math Problem Analysis
Mathematical Concepts
Complex Analysis
Cauchy Integral Formula
Contours
Analytic Functions
Formulas
Cauchy Integral Formula: \( f(a) = \frac{1}{2\pi i} \oint_C \frac{f(z)}{z - a} \, dz \)
\( \oint_C \frac{f(z)}{z - a} \, dz = 2\pi i f(a) \)
Theorems
Cauchy-Goursat Theorem
Cauchy Integral Formula
Suitable Grade Level
Undergraduate (Advanced Calculus or Complex Analysis)
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