Fundamental Theorem of Complex Calculus
Hello everyone, I was having trouble with the proof of this and I was wondering if anyone could help me!
Let be analytic (where S is an open set), and such that if is a piecewise continuously differentiable path in S, then if f' is continuous on (which is always true anyway), and
PROOF: Write as , where each is a simple smooth path, with
Then now here I have a problem because it says this line is equal to
by the fundamental theorem of calculus for REAL functions. however is not real valued is it? so why can i use it here?