GATE 2022 MA – Question 29

Complex Analysis · Complex Integration and Residues · 1 mark · Numerical answer

How many zeros, counting multiplicity, does 2z⁷−7z⁵+2z³−z+1 have in |z|<1?

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Correct answer: 5 to 5

Explanation

On |z|=1 the term −7z⁵ has modulus 7, while the sum of the moduli of the remaining terms is at most 2+2+1+1=6. Rouché gives the same zero count as −7z⁵: **5**.

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