Teaching JKPSC Lecturership Mock Test Series 2024-25 Mathematical Science Complex Analysis Analytic Functions
Let f be an entire function that satisfies |f(z)| ≤ ey for all z = x + iy ∈ ℂ, where x, y ∈ ℝ. Which of the following statements is true?
1
f(z) = ce−iz for some c ∈ ℂ with |c| ≤ 1.
2
f(z) = ceiz for some c ∈ ℂ with |c| ≤ 1.
3
f(z) = e−ciz for some c ∈ ℂ with |c| ≤ 1.
4
f(z) = eciz for some c ∈ ℂ with |c| ≤ 1.