Which of the following maps are constant?
(a) $f : D → C$ such that $f$ is analytic and $f(D) ⊂ R.$
(b) $f : D → D$ such that $f$ is analytic and $f([−1/2, 1/2])$ = {0}.
(c) $f : C → C$ such that $f$ is analytic and $Re(f)$ is bounded.
(d) $f : C → C$ such that $f$ is analytic and $f$ is bounded on the real and imaginary axes
*My works *:
option a),b) and c) will true by Liouville's theorem that is real value and analytics implies constant
option d) will be false take $f(z) =e^{iz^2}$
Please verify whether I am right /wrong ? Thanks in advanced.
Yes I'm right, my answer is correct