Teaching CSIR NET Mock Test Series Mathematical Science Complex Analysis Analytic Functions

Let ℍ = {z ∈ ℂ : Im(z) > 0} denote the upper half plane and let f : ℂ → ℂ be defined by f(z) = eiz. Which one of the following statements is true? 

1
f(ℍ) = ℂ\{0}. 
2
f(ℍ) ∩ ℍ is countable. 
3
f(ℍ) is bounded. 
4
f(ℍ)is a convex subset of ℂ. 
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