Let f be an entire function on ℂ and let Ω be a bounded open subset of ℂ. Let S = {Re f(z) + Im f(z)| z ∈ Ω}. Which of the following statements is/are necessarily correct?
1
S is an open set in ℝ
2
S is a closed set in ℝ
3
S is an open set of ℂ
4
S is a discrete set in ℝ