10.6.29 Analytic functions
condition: Find and draw on the plane \( (\alpha ; \beta) \) areas in which the number of roots of the polynomial \( P(z)=z^{3}+(\alpha+\beta) z^{2}+(\alpha+\beta) z+\alpha \) having a positive real part is constant.
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.