Question 4. Let R > 0 be a real number and let CR denote the semicircular arc of radius R in the upper half of the complex plane centred at the origin from R to -R. -R C R Use lemma 3.2.9 to prove that SCH 1 z² +4 dz 0 as R→ ∞. [5 marks] Question 5. (a) Show that there does not exist a holomorphic function F: C\{0} → C such that F' (z) = 1/z for all non-zero z = C. (b) Deduce that there does not exist a holomorphic function L: C\{0} → C such that exp(L(z)) = z for all non-zero z Є C. [5 marks]

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