Complex Analysis: Theory and Applications · Problem 8.7.3

Conformal Mapping — Howell & Matthews

Mathematics — Complex Analysis · rouche-theorem

Problem

Let g(z)=z5+4z−15g(z) = z^5 + 4z - 15. (a) Show that there are no zeros in D1(0)D_1(0). (b) Show that there are five zeros in D2(0)D_2(0). Hint: Consider f(z)=−z5f(z) = -z^5. Remark: A factorization of the polynomial using numerical approximations for the coefficients is (z−1.546)(z2−1.340z+2.857)(z2+2.885z+3.397).(z - 1.546)(z^2 - 1.340z + 2.857)(z^2 + 2.885z + 3.397).

Related theory

Browse the problem library