
10.6.6 Analytic functions
Problem:
Prove that there is an analytic function with a given real \( (u(x, y)) \) or imaginary \( (v(x, y)) \) part and restore it under the given condition \( f\left(z_{0}\right)=z_{1} \).
\[
\begin{array}{l}
v(x, y)=3 x^{2} y-y^{3}+6 x y+3 y+2, \\
f(-i)=-3 .
\end{array}
\]