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X Find all complex solutions to |z + 2| = |2 - 2i and sketch the solution set.

X Find all complex solutions to |z + 2| = |2 - 2i and sketch the solution set.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 26E
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X Find all complex solutions to |z + 2| = |2 – 2i| and sketch the solution set. X Let LCC be the line r = 1. Prove that if f: C + L is analytic, then f is constant. S- Recall that M(r, f) = max;l=r\f(2)|. For this question, let f(z) = sin z. A Find the real and imaginary parts of f(z). 64) Hence, or otherwise, find a formula for M(r, f) in terms of r only. jin Show that M(r, f) is strictly increasing inr. DA Which theorem implies that (iii) is always true for non-constant entire functions?
Transcribed Image Text:X Find all complex solutions to |z + 2| = |2 – 2i| and sketch the solution set. X Let LCC be the line r = 1. Prove that if f: C + L is analytic, then f is constant. S- Recall that M(r, f) = max;l=r\f(2)|. For this question, let f(z) = sin z. A Find the real and imaginary parts of f(z). 64) Hence, or otherwise, find a formula for M(r, f) in terms of r only. jin Show that M(r, f) is strictly increasing inr. DA Which theorem implies that (iii) is always true for non-constant entire functions?
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