Complex analysis

Let f(z)= z bar. This is an example of a function which is continuous everywhere but does NOT possess an antiderivative. To demonstrate this fact it suffices to show that the integral z bar dz is not path independent. Consider two paths: C1: the straight path from z=-1 towards z=i. Let C2 be the sequence of straight line paths along the Real axis followed by the straight line path along the Imaginary axis. Parameterize these paths and show the values do not agree. Explain how this demonstrates that there is no antiderivative for f(z)=z bar.

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