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 - constant.
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.