Part CCSIR NET December 2024multiply-by-one-minus-i-to-fix-the-real-part

Multiply by one minus i to fix the real part

For z = x + iy $\in \mathbb{C}$ , let f(z) = u(x, y) + iv(x, y) be an entire function such that u(x, y) + v(x, y) = 1. Which of the following statements are FALSE?

A.f is a constant function.
B.If $f(0) \in \mathbb{R}$ , then f(0) + f(1) = 1.✓ Correct
C. $f(\mathbb{C})$ is connected.
D.If $f(2) \in \mathbb{R}$ , then f(i) + f(1) = 2.

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 execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Multiply by one minus i to fix the real part

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