Question Bank MSQ • 2 Marks Section 1: Mathematical Physics Complex analysis

QB_PH_012: Complex analysis

Question Statement

Which of the following complex functions is/are analytic everywhere in the complex plane $\mathbb{C}$?
(A) f(z) = e^z
(B) f(z) = \sin(z)
(C) f(z) = |z|^2
(D) f(z) = z^*
Correct Answer
A, B
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $e^z$ and $\sin(z)$ are entire functions. $|z|^2$ and $z^*$ are nowhere analytic.
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