10.6.26 Analytic functions
Condition: Determine whether a given function can serve as a real or imaginary part of some regular function and if so, then restore this regular function as \( f(z) \). Make sure that the found function is regular and satisfies the given condition. In the condition: \( U(x, y) \) is the real part, \( V(x, y)- \) is the imaginary part. \[ V(x, y)=\operatorname{ch}(2 x) \cos (2 y) \]
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.