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5) Using Ex 9.5 from Lecture Notes determine which of the following functions are entire. Justify your answer: i) cos (21² v) Imz

5) Using Ex 9.5 from Lecture Notes determine which of the following functions are entire. Justify your answer: i) cos (21² v) Imz

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)
Problem 29E
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qu 5 i,v

resource ex 9.5 attached 

Ex 9.5: Prove: if f(z) is analytic and real on a domain R then I is a constant function.. Pf: I is analytic and real on √2 => f(x,y) = u(x, y) +².0 namely v(x, y) = 0₁ CR equations hold for I from analyticity on 1}: every ZEN 04 OV = 0 and and Dy = - DV=0 24 = DU = 0 => M(X,Y) = CER = f(x,y)=c, namely if is a constant function.
Transcribed Image Text:Ex 9.5: Prove: if f(z) is analytic and real on a domain R then I is a constant function.. Pf: I is analytic and real on √2 => f(x,y) = u(x, y) +².0 namely v(x, y) = 0₁ CR equations hold for I from analyticity on 1}: every ZEN 04 OV = 0 and and Dy = - DV=0 24 = DU = 0 => M(X,Y) = CER = f(x,y)=c, namely if is a constant function.
5) Using Ex 9.5 from Lecture Notes determine which of the following functions are entire. Justify your answer: i) cos 121² v) Imz
Transcribed Image Text:5) Using Ex 9.5 from Lecture Notes determine which of the following functions are entire. Justify your answer: i) cos 121² v) Imz
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