Question: Consider the open set C{0}, which is not simply connected, and for each E C the holomorphic function fi(z) = ( + 4) e.

$Consider the open set C\{0}, which is not simply connected, and for$ each E C the holomorphic function fi(z) = ( + 4) e.

Consider the open set C\{0}, which is not simply connected, and for each E C the holomorphic function fi(z) = ( + 4) e. The Cauchy Residue Theorem implies that there is a unique value o of such that Jy J, (z) dz = 0 for every closed contour Y C C\{0}. Which of the following statements is correct? Select one: A0 = 0 but fo(z) does not have a primitive Fo(z) on C\{0}. Ao = -2 but f-2(z) does not have a primitive Fo(z) on C\{0}. Ao = 0 and fo(z) has primitive Fo(z) on C\{0} with Laurent expansion around 0 C beginning +1+... 20 = -2 and f-2(z) has a primitive Fo(z) on C\{0} with Laurent expansion around 0 EC beginning 1-2-3+. None of the others 20 = 1 and fo(z) has primitive F(z) on C\{0} with Laurent expansion beginning - /2 + 2i + ....

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