Discussion
Consider the following statements about analytic functions. 1. The real and imaginary parts are both harmonic 2. The Cauchy-Riemann equations alone guarantee analyticity 3. An analytic function is infinitely differentiable
Answer: D
The first and third hold, the third being one of the striking differences from real analysis. The second omits a hypothesis: the equations must be accompanied by continuity of the partial derivatives, without which functions exist that satisfy them at a point yet are not differentiable there
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