#ComplexAnalysis

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#ComplexAnalysis || #Laurent’s Theorem #education #trending #share ||M Sc Mathematics, Sem 1|| Unit III || Value For Time || Kamal Kumar
Some important Examples based on Rouche's Theorem
Rouche's Theorem: If 𝒇(𝒛) and 𝒈(𝒛) are analytic inside and on a closed
contour C and |𝒈(𝒛)| is less than |𝒇(𝒛)| on 𝑪, then 𝒇(𝒛) and 𝒇(𝒛) + 𝒈(𝒛) have the same number of zeros inside 𝑪.
Q. Prove that the polynomial 𝒇(𝒛)=𝒛^𝟒+𝒛^𝟑+𝟏 has only one zero in the first
quadrant of the complex plane.
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