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Counterexample bank

Part C is won by knowing which tempting claims are false. 148 counterexamples; 85 free. The rest come with the Notes pack.

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#1 · Complex Analysis, Algebra & Topology › Singularities and Residues

“∮_γ f = 0 implies f is holomorphic inside γ” — false

Counterexample locked — unlock with Notes + PYQ

complexresidues

#2 · Complex Analysis, Algebra & Topology › Singularities and Residues

“A small indentation around a simple pole contributes 2πi·Res” — false

Counterexample: The indentation at 0 when computing ∫₀^∞ sin x/x dx

A half-circle contributes $iπ \cdot$ Res; using $2 π i$ gives twice the right answer.

complexresidues