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2.3: Diferenciación compleja
https://espanol.libretexts.org/Matematicas/Analisis/An%C3%A1lisis_Complejos_-_Una_Introducci%C3%B3n_Visual_e_Interactiva_(Ponce_Campuzano)/02%3A_Cap%C3%ADtulo_2/2.03%3A_Diferenciaci%C3%B3n_compleja
\({f}'\left ( z_{0} \right )=\lim_{k\rightarrow 0}\frac{f\left ( z_{0}+ik \right )-f\left ( z_{0} \right )}{ik}=\lim_{k\rightarrow 0}\left [ -i\frac{f\left ( x_{0}+i\left ( y_{0} +k\right )\right )-f\... ${f}'\left ( z_{0} \right )=\lim_{k\rightarrow 0}\frac{f\left ( z_{0}+ik \right )-f\left ( z_{0} \right )}{ik}=\lim_{k\rightarrow 0}\left [ -i\frac{f\left ( x_{0}+i\left ( y_{0} +k\right )\right )-f\left ( x_{_{0}}+iy_{0} \right )}{k}\right ]\\=\lim_{k\rightarrow 0}\left [ \frac{v\left ( x_{0},y_{0}+k \right )-v\left ( x_{0},y_{0} \right )}{k} -i\frac{u\left ( x_{0},y_{0}+k \right )-u\left (x_{0},y_{0} \right )}{k}\right ]\\=v_{y}\left ( x_{0},y_{0} \right )-iu_{y}\left ( x_{0},y_{0} \right )$

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