10.6.25 Analytic functions
condition: Check whether the given function is regular. For a regular function, find the derivative using the formula. \[ F(z)=\frac{d u}{d x}+i \frac{d v}{d x} \mid \begin{array}{l} x=z \\ y=0 \end{array}, \quad F(z)=\ln (\bar{z}-1)\text {. } \]
Differentiation of analytical functions, finding their real and imaginary parts, finding the number of roots of complex equations using the argument principle, Roucher's theorem and much more in this section.