attached is homework assignment in "complex functions" university course.
i need a full and detailed solution.
notice that Z is a complex number
1. Calculate the following:
2. Find all the solutions for the following equations:
3. Given that:
4. Assuming the radius of convergence of the power series ∑ 𝑐 𝑧 is R. Calculate the radius of convergence for the following power series:
5. Calculate the radius of convergence for the following power series:
6. Find the Holomorphic function f(z) if the following is given:
a . b . c . d . e . f .
7. Prove that if 𝑓(𝑧) and 𝑓̅(𝑧) are Holomorphic functions in domain D, than 𝑓(𝑧) is a constant function.
8. Prove that if 𝑓(𝑧) and 𝑔(𝑧) are Holomorphic functions in domain D, than
𝐼𝑚 𝑓(𝑧) + �̅�(𝑧) = 0 if and only if 𝑓(𝑧) − 𝑔(𝑧) = 𝐶 in domain D and C is a Real constant.
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