Review: Log, Roots, Continuous Complex-Valued Function, Mean Value Theorem etc.

Please assist with the attached problems, such as: 4. By chooseing specific nonzero values of z1 and z2, show that ... is not always valid when log is replaced by Log.

Evaluating Integrals by Cauchy-Goursat Theorem

Evaluating integrals by Cauchy-Goursat Theorem. See attached for full problem description.

Three problems.

2. Suppose that f(z) is entire and that the harmonic function... Show that u(x,y) must be constant throughout the plane... See the attachment for all problems.

two problems.(Complex variables)

2. Derive the Laurent series representation... Please see attached.

complex variables (evaluation problems).

See the attachment for the problems. Thank you