5. Find the pair of complex numbers Z1 and z2 such that Log (z12)* Log z + Log z2 where Log z represents the principal value of logz. Is Log(1 +i)(1 -i) = Log (1 +i) + Log(1- i)? Justify your answer. Expand the functions z3 - 6z+ 7z-3 into a Taylor series about the point Zo = 1. Give two Laurent series expansions in powers of z for the function Z J)(z-1)(7-2) and specify the regions in which those expansions are valid.