Question

Which of the following statements are correct:
A. $e^{-x}(x \sin y - y \cos y)$ is harmonic B. $f(z) = u + iv$ is analytic, where $u = x, v = y$.
C. $f(z) = z^{1/2}$ is analytic on $\mathbb{C}$. D. $f(z) = \frac{1}{z}$ is not analytic on $\mathbb{C}$. E. $f(z) = \sin(z^3)$ is bounded.
Choose the correct answer from the options given below:

• A. A, C, E Only
• B. A, B, D Only
• C. A, B, C Only
• D. A, D, E Only

Hint:

Remember Liouville's Theorem: Non-constant entire functions like $\sin(z^3)$ or $e^z$ are NEVER bounded on $\mathbb{C}$!

Answer 1

The Correct Option is B