Part CCSIR NET December 2024only-multiples-of-four-survive

Only multiples of four survive

Let $f : C \to C$ be an entire function such that f(z) = f(iz) for all $z \in C$ . Which of the following statements are true?

A.f(z) = f(−z) for all $z \in C$ .✓
B.f′(0) = f″(0) = f‴(0) = 0✓
C.There is an entire function $g : C \to C$ such that $f (z) = g (z^{4})$ for all $z \in C$ .✓
D.f is necessarily a constant function.

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

50 are analysed free — try those first.

More on this topic