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Part BCSIR NET December 2023

Cauchy–Riemann equations, harmonic functions

Let ℍ = { $z \in C : I m z > 0$ } and f(z) = $e^{i z}$ . Which one of the following statements is true?

A.f(ℍ $) = C$ ∖{0}.
B.f(ℍ) ∩ ℍ is countable.
C.f(ℍ) is bounded.
D.f(ℍ) is a convex subset of $C$ .

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Related counterexample: A harmonic function on any domain has a harmonic conjugate

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From Analytic Functions › Cauchy–Riemann equations, harmonic functions

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