1. Calculate the following:
2. Find all the solutions for the following equations:
3. Given that:
Prove that:
4. Assuming the radius of convergence of the power series ∑ ஶ
ୀ 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 ( ) and ̅( ) are Holomorphic functions in domain D, than ( ) is a
constant function.
8. Prove that if ( ) and ( ) are Holomorphic functions in domain D, than
൫ ( ) + ̅( )൯ = 0 if and only if ( ) − ( ) = in domain D and C is a Real constant.
Homework Assignment In “Complex Functions”