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State Liouville's Theorem on entire functions and the Maximum Modulus Principle. Let p(z) = z″ + an−12″ ¹ + ... + a1z + ao be a nonconstant polynomial. Show that there is a number R> 0 such that |2|n |p(z)|≥ for |z|> R. 2 By considering f(z) = in C. P(2) and using the results above, deduce that p has a zero

State Liouville's Theorem on entire functions and the Maximum Modulus Principle. Let p(z) = z″ + an−12″ ¹ + ... + a1z + ao be a nonconstant polynomial. Show that there is a number R> 0 such that |2|n |p(z)|≥ for |z|> R. 2 By considering f(z) = in C. P(2) and using the results above, deduce that p has a zero

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.5: Systems Of Linear Equations In More Than Two Variables
Problem 44E
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State Liouville's Theorem on entire functions and the Maximum Modulus Principle. Let p(z) = z″ + an−12″ ¹ + ... + a1z + ao be a nonconstant polynomial. Show that there is a number R> 0 such that |2|n |p(z)|≥ for |z|> R. 2 By considering f(z) = in C. P(2) and using the results above, deduce that p has a zero
Transcribed Image Text:State Liouville's Theorem on entire functions and the Maximum Modulus Principle. Let p(z) = z″ + an−12″ ¹ + ... + a1z + ao be a nonconstant polynomial. Show that there is a number R> 0 such that |2|n |p(z)|≥ for |z|> R. 2 By considering f(z) = in C. P(2) and using the results above, deduce that p has a zero
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