MathProblemsBank

10.6.12 Analytic functions

Problem: Using Rouche's theorem, find the number of roots of the equation in disk \( D(0 ; R) \). a) \( z^{3}+z+1=0, \quad R=\frac{1}{2} \). b) \( z^{2}-\cos z=0, \quad R=2 \).