COMPLEX ANALYSIS 1

III.2.5. Derive the formulas 812 + 812 ' 811 _ 811 cosz= and smz=_ 2 21 III.2.11. Suppose f : G > C is a branch of the logarithm and that n E Z. prove that z\" = exp(nf(z)) for all z E G. 111.2.12. Prove that the real part of z\": = exp(% log 3) (where log 2 is the principal branch of log) is positive)