Page "Cauchy–Riemann equations" Paragraph 26
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Conversely, if ƒ: C → C is a function which is differentiable when regarded as a function on R < sup > 2 </ sup >, then ƒ is complex differentiable if and only if the Cauchy – Riemann equations hold.
In other words, if u and v are real-differentiable functions of two real variables, obviously u + iv is a ( complex-valued ) real-differentiable function, but u + iv is complex-differentiable if and only if the Cauchy – Riemann equations hold.
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