Mathematics · Complex Analysis
Let f be an entire function such that for every integer k ≥ 1 there is an infinite set X k such that f(z) = 1 k for all z ∈ X k . Which of the following statements is necessarily true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
Share:
- 1If there exists a bounded sequence (z k ) k≥1 such that z k ∈ X k for each k ≥ 1, then f has a zero✓
- 2The set X k is unbounded for each k ≥ 1
- 3There exists a non-empty closed set X such that f(z) = 0 for all z ∈ X
- 4There exists an infinite set X such that f(z) = 0 for all z ∈ X
Correct answer
If there exists a bounded sequence (z k ) k≥1 such that z k ∈ X k for each k ≥ 1, then f has a zero
Download Single Question PDF
Save this question and verified answer as a clean study sheet with live clickable link.
👥
Share with Friends & Study Groups
Challenge your peer aspirants on WhatsApp or Telegram to solve this question!
Online Test Series
Start Free Mock Test →Preparing for Mathematics?
Practice full-length mock tests with real exam timers, instant score analysis, and all-India ranking.
Chapter Practice
Practice Complex Analysis MCQs →Want more practice questions on Complex Analysis?
Solve complete topic-wise tests with detailed solutions on GkGet.
Related Practice Questions
Recommended practice questions in Mathematics · Complex Analysis