10.6.23 Analytic functions
Condition: At what values of the parameter \( a \) is this function a real (imaginary) part of some analytic function. Find this feature. \[ u=x^{2}-a y^{2}+x y \]
Differentiation of analytic 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.