10. Find all possible solutions of the equation cos z = 2/15. 11. Let F be the branch of log z, which is analytic in the

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10 Find All Possible Solutions Of The Equation Cos Z 2 15 11 Let F Be The Branch Of Log Z Which Is Analytic In The 1 (23.94 KiB) Viewed 42 times

10. Find all possible solutions of the equation cos z = 2/15. 11. Let F be the branch of log z, which is analytic in the domain created by the branch cut y = 3,7 2 0 and such that F(1) = 6i. Find F(-2) and F(-V3+ i). 12. Read the following proposition and its proof on p.97 and then answer the questions which follow: Proposition. If : and w are nonzero complex numbers, then log zu = long 2 + log w. (a) How is this equality to be interpreted? (b) Why is it necessary that we specify how this equality is to be interpreted? (e) How do we know that in zwl + i arg zu = In 1=1 + i arg : + Inw + i arg w? (d) Is it always true that Log zw = Log z + Log w? ܀