2017 | OriginalPaper | Chapter
ℝ- and ℂ-Differentiability
Author : Alexander Isaev
Published in: Twenty-One Lectures on Complex Analysis
Publisher: Springer International Publishing
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Let z0 = x0+iy0 = (x0,y0) be a point in $$ \mathbb{C} $$ and f a function defined on a neighbourhood of z0 (e.g., on an open disk $$ \varDelta(z_{0},\ r) $$ for some r > 0) with values in $$ \mathbb{C} $$ . Write $$ f(z) = \mathrm{Re}\ f(z)+i\mathrm{Im}\ f(z) = u(z)+iv(z) = u(x,y)+iv(x,y) $$ .