complez variables class Rouches Thm **Problem 24:** Determine the number of zeroes of the polynomial $ z^7 - 6z^5 + 8 $ in the annulus $ 1 \leq |z| \leq 2 $.*Explanation:* This problem involves finding the roots of the given polynomial within a specified annular region in the complex plane. The annulus is defined by the inequalities $ 1 \leq |z| \leq 2 $, representing the area between two concentric circles with radii 1 and 2. The goal is to calculate how many roots of the polynomial lie within this region.

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Answered: 24. Determine the number of zeroes of…

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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24. Determine the number of zeroes of the polynomial z7 – 6z5 + 8 in the annulus 1 < |z| < 2.