Question

8. ExTRA CREDIT. Let Vz be the branch of the square root function defined in Question 3 of Project 4, with domain the entire complex plane C. Find a subdomain Ω of C such that the formula V212VVz2 would hold for any z1,z2 S2. Show why the formula tails in all of C, and provide concrete examples. Generalize your answer for the case when the branch of chosen so that Carg%, α + 2π, where α is any fixed real number, always setting VO 0, Discuss the particular case α 0 To get credit for this question you must provide complete and detailed discussions and explanations.

Answer 1

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