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fi" (0) = 5² +1 = 26 etc. You can see very quickly that the moduli of these numbers grow beyond any bounds as n → 0. So this tells us that 1 4 M. Your job is to determine whether i E M. Show your work. Here is a picture of the Mandelbrot Set:

fi" (0) = 5² +1 = 26 etc. You can see very quickly that the moduli of these numbers grow beyond any bounds as n → 0. So this tells us that 1 4 M. Your job is to determine whether i E M. Show your work. Here is a picture of the Mandelbrot Set:

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Safari File Edit View History Bookmarks Window Help 73% (4) Thu 01:15 A learn-eu-central-1-prod-fleet01-xythos.content.blackboardcdn.com Content B https://learn-eu-central-1-prod-fleet01-x.. B https://learn-eu-central-1-prod-fleet01. B https://learn-eu-central-1-prod-fleet01.. -1+i Let z = 2, (i) Determine the modul... f(4 (0) = 52 + 1 = 26 etc. You can see very quickly that the moduli of these numbers grow beyond any bounds as n → ∞. So this tells us that 1 ¢ M. Your job is to determine whether i E M. Show your work. Here is a picture of the Mandelbrot Set: Created by Wolfgang Beyer with the program Ultra Fractal 3., A DEC W ng ol
Transcribed Image Text:Safari File Edit View History Bookmarks Window Help 73% (4) Thu 01:15 A learn-eu-central-1-prod-fleet01-xythos.content.blackboardcdn.com Content B https://learn-eu-central-1-prod-fleet01-x.. B https://learn-eu-central-1-prod-fleet01. B https://learn-eu-central-1-prod-fleet01.. -1+i Let z = 2, (i) Determine the modul... f(4 (0) = 52 + 1 = 26 etc. You can see very quickly that the moduli of these numbers grow beyond any bounds as n → ∞. So this tells us that 1 ¢ M. Your job is to determine whether i E M. Show your work. Here is a picture of the Mandelbrot Set: Created by Wolfgang Beyer with the program Ultra Fractal 3., A DEC W ng ol
Safari File Edit View History Bookmarks Window Help 73% (4) Thu 01:14 A learn-eu-central-1-prod-fleet01-xythos.content.blackboardcdn.com Content B https://learn-eu-central-1-prod-fleet01-x.. B https://learn-eu-central-1-prod-fleet01.. B https://learn-eu-central-1-prod-fleet01.. b -1+i Let z = 2, (i) Determine the modul... 5. (The answer to this question is MUCH shorter than the question itself.) The Mandelbrot Set M is a subset of the complex plane defined as follows: Given c E C, consider the function 6 fc: C → C H 22 + c and define f (2) = fe(fc(… fe(2))); felfe(.. n times i.e. the function f) is the function f. composed with itself n times. Then M = {c € C : |f!") (0)| is bounded as n → 0}. (We have not defined what 'bounded' means, but you can use your intuition here.) So, for example, if we look at c= 1, and want to determine whether 1 E M or not, we need to check the moduli of the numbers f1(0) = 0² + 1 = 1 (0) = f1(fi(0)) = f1(1) = 1² +1 = 2 (3) f (0) = 22 + 1 = 5 A DEC W ng
Transcribed Image Text:Safari File Edit View History Bookmarks Window Help 73% (4) Thu 01:14 A learn-eu-central-1-prod-fleet01-xythos.content.blackboardcdn.com Content B https://learn-eu-central-1-prod-fleet01-x.. B https://learn-eu-central-1-prod-fleet01.. B https://learn-eu-central-1-prod-fleet01.. b -1+i Let z = 2, (i) Determine the modul... 5. (The answer to this question is MUCH shorter than the question itself.) The Mandelbrot Set M is a subset of the complex plane defined as follows: Given c E C, consider the function 6 fc: C → C H 22 + c and define f (2) = fe(fc(… fe(2))); felfe(.. n times i.e. the function f) is the function f. composed with itself n times. Then M = {c € C : |f!") (0)| is bounded as n → 0}. (We have not defined what 'bounded' means, but you can use your intuition here.) So, for example, if we look at c= 1, and want to determine whether 1 E M or not, we need to check the moduli of the numbers f1(0) = 0² + 1 = 1 (0) = f1(fi(0)) = f1(1) = 1² +1 = 2 (3) f (0) = 22 + 1 = 5 A DEC W ng
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