Complex Analysis: Theory and Applications · Problem 8.7.4

Conformal Mapping — Howell & Matthews

Mathematics — Complex Analysis · rouche-theorem

Problem

Let g(z)=z3+9z+27g(z) = z^3 + 9z + 27. (a) Show that there are no zeros in D2(0)D_2(0). (b) Show that there are three zeros in D4(0)D_4(0). Remark: A factorization of the polynomial using numerical approximations for the coefficients is (z+2.047)(z2−2.047z+13.19).(z + 2.047)(z^2 - 2.047z + 13.19).

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