Counterexample

Is this true?

A harmonic function on any domain has a harmonic conjugate

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

86 counterexamples are free — including most of the ones Part C leans on hardest.

Keep practicing

Hypothesis dropped

A theorem applied without checking one of its preconditions.

See real exam options built on this mistake Drill statements like this

complex harmonic

Go deeper· Explained in full in Cauchy–Riemann — what they do and do not give you· Asked in CSIR NET December 2024· From Analytic Functions › Cauchy–Riemann equations, harmonic functions

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