Complex Analysis: Theory and Applications · Problem 8.7.2

Conformal Mapping — Howell & Matthews

Mathematics — Complex Analysis · rouche-theorem

Problem

Show that four of the five roots of the equation z5+15z+1=0z^5 + 15z + 1 = 0 belong to the annulus A ⁣(0,32,2)={z:32<∣z∣<2}.A\!\left(0,\tfrac{3}{2},2\right) = \left\{z : \tfrac{3}{2} < |z| < 2\right\}.

Related theory

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