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Primitive F and Cauchy Riemann Equations

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Let for . Prove in the following two ways that f has no primitive:

a) Assume that f has a primitive F (i.e. these is an entire function F with F'(z)=f(z) for all z). Show that f then would have to satisfy the Cauchy-Riemann equations. Check that f does not satisfy these equations.
b) Assume that f has primitive F. then integrals along closed curves C must vanish. Find a c such that the integral does not vanish.

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Primitive F and Cauchy Riemann Equations are investigated. The solution is detailed and well presented.

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Proof:
(a) If has a primitive , i.e. there is an entire ...

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