Part BCSIR NET June 2025the-line-misses-the-origin-so-the-forced-constant-is-non-zero

The line misses the origin so the forced constant is non zero

Let f be an entire function such that $f (C) \subset$ {x + iy | y = x + 1}. Which of the following statements is true?

A.|f(z)| $\to \infty$ as |z| $\to \infty$ .
B.f(z)/z → 0 as |z| $\to \infty$ .✓
C.zf(z) → 0 as |z| $\to \infty$ .
D.f(z) → 0 as |z| $\to \infty$ .

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, and why this one tests boundary and endpoint.

See pricing

50 are analysed free — try those first.

The trap it tests

Boundary and endpoint

The statement turns at the edge of the interval, the domain, or the parameter range.

Drill statements like this

The line misses the origin so the forced constant is non zero

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