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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 › Analytic Functions

“The Cauchy–Riemann equations at a point imply complex differentiability there” — false

Counterexample: f(z) = (z̄)²/z for z ≠ 0, f(0) = 0

CR hold at 0, but the difference quotient along z = t(1+i) differs from the one along the real axis.

complexcauchy-riemann