The order of 16 in \((\mathbb{Z}_{24}, +_{24})\) is:
- 2
- 3
- 4
- 6
The Correct Option is B
Solution and Explanation
Top Questions on Complex Functions
Let \( \Omega \) be a non-empty open connected subset of \( \mathbb{C} \) and \( f: \Omega \to \mathbb{C} \) be a non-constant function. Let the functions \( f^2: \Omega \to \mathbb{C} \) and \( f^3: \Omega \to \mathbb{C} \) be defined by \[ f^2(z) = (f(z))^2 \quad {and} \quad f^3(z) = (f(z))^3, \quad z \in \Omega. \]
Consider the following two statements:
S1: If \( f \) is continuous in \( \Omega \) and \( f^2 \) is analytic in \( \Omega \), then \( f \) is analytic in \( \Omega \).
S2: If \( f^2 \) and \( f^3 \) are analytic in \( \Omega \), then \( f \) is analytic in \( \Omega \). Then, which one of the following is correct?- GATE MA - 2025
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Let \( U = \{z \in \mathbb{C}: \operatorname{Im}(z) > 0\} \) and \( D = \{z \in \mathbb{C}: |z| < 1\} \), where \( \operatorname{Im}(z) \) denotes the imaginary part of \( z \).
Let \( S \) be the set of all bijective analytic functions \( f: U \to D \) such that \( f(i) = 0 \).
Then, the value of \( \sup_{f \in S} |f(4i)| \) is:- GATE MA - 2025
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x 0 1 2 3 4 y(x) 1 3 6 9 12 - GATE PI - 2024
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