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Cauchy - Riemannovi Uslovi
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Cauchy-Riemannovi uslovi
𝑍 = 𝑥 + 𝑖𝑦 𝑍 = 𝜌𝑒𝑖𝜑
𝑓(𝑍) = 𝑢(𝑍) + 𝑖𝑣(𝑍)
𝑑𝑢𝑑𝑥
=𝑑𝑣𝑑𝑦
𝑑𝑢𝑑𝑦
= −𝑑𝑣𝑑𝑥
𝜌𝑑𝑢𝑑𝜌
= 𝑑𝑣𝑑𝜑
𝑑𝑢𝑑𝜑
= −𝜌𝑑𝑣𝑑𝜌
𝑓(𝑍) = 𝑅(𝑍)𝑒𝑖𝜃(𝑍)
𝑑𝑅𝑑𝑥
= 𝑅𝑑𝜃𝑑𝑦
𝑑𝑅𝑑𝑦
= −𝑅𝑑𝜃𝑑𝑥
𝜌𝑑𝑅𝑑𝜌
= 𝑅 𝑑𝜃𝑑𝜑
𝑑𝑅𝑑𝜑
= −𝑅𝜌𝑑𝜃𝑑𝜌
