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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Answered: X Find all complex solutions to |z + 2|…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter13: Conic Sections

Section13.1: Circles

Problem 48PS

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24.If the functions y1 and y2 are a fundamental set of solutions of y″ + p(t) y′ + q(t) y = 0, show that between consecutive zeros of y1 there is one and only one zero of y2. Note that this result is illustrated by the solutions y1(t) = cos t and y2(t) = sin t of the equation y″ + y = 0. Hint: Suppose that t1 and t2 are two zeros of y1 between which there are no zeros of y2. Apply Rolle's theorem to y1/ y2 to reach a contradiction. Change of Variables. Sometimes a differential equation with variable coefficients, (32) y′′+p(t)y′+q(t)y=0 can be put in a more suitable form for finding a solution by making a change of the independent variable. We explore these ideas in Problems 25 through 36. In particular, in Problem 25 we show that a class of equations known as Euler equations can be transformed into equations with constant coefficients by a simple change of the independent variable. Problems 26 through 31 are examples of this type of equation. Problem 32 determines conditions under…
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X Find all complex solutions to |z + 2| = |2 - 2i and sketch the solution set.