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Find all the solutions of cos z = 1+i. Make sure that the solutions you obtained checks out with the given equation.

Find all the solutions of cos z = 1+i. Make sure that the solutions you obtained checks out with the given equation.

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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Answer the following questions. Show details of your work. Find all the solutions of cos z = 1+i. Make sure that the solutions you obtained checks out with the given equation. b Evaluate the expression sin(4 + 3i) · cos(3 + 4i). a Rewrite exp(2 + Злі) exp(-3 + пі/2) in the form x + yi. Find all the values of z that satisfy the equation ez-1 = -ie?. Make sure that the solutions you obtained checks out with the d given equation. Show that (a) Isinh z|2 = sin? y + sinh? x; (b) |cosh z|2 = cos? y + sinh? x; and (c) the function tanh z is periodic with period %3D e ni.
Transcribed Image Text:Answer the following questions. Show details of your work. Find all the solutions of cos z = 1+i. Make sure that the solutions you obtained checks out with the given equation. b Evaluate the expression sin(4 + 3i) · cos(3 + 4i). a Rewrite exp(2 + Злі) exp(-3 + пі/2) in the form x + yi. Find all the values of z that satisfy the equation ez-1 = -ie?. Make sure that the solutions you obtained checks out with the d given equation. Show that (a) Isinh z|2 = sin? y + sinh? x; (b) |cosh z|2 = cos? y + sinh? x; and (c) the function tanh z is periodic with period %3D e ni.
Answer the following questions. Show details of your work Evaluate L(5 cosh 2t – 3 sinh t), L(t?e-2 + e-2 cos 2t + 3e-24), and L(10e transform as a ratio of two polynomials. b Evaluate L-1 -4* cos ( 3t -) sin ( 4t +)). Express the a s+8 (?(52+16), £² ( s, and L-1 52+4s+5, s++5s3+18s2+34s+20, Solve the initial value problem y" + y" + y' +y = cos 3t with y(0) = 0, y'(0) = 1, and y" (0) = 1 using Laplace transform methods. Solve the initial value problem y" + 3y' + 2y = 2u(t – 2) d with y(0) = 0 and y'(0) = 0 using Laplace transform methods. Plot the solution and the input r(t) = 2u(t – 2) on the same set of axis. Comment on the results. Solve the initial value problem y" + 4y = 8(t – 1) – 8(t – 2n) with y(0) = 1 and y' (0) = 0 using Laplace transform methods. Plot the solution and comment on the results. %3D
Transcribed Image Text:Answer the following questions. Show details of your work Evaluate L(5 cosh 2t – 3 sinh t), L(t?e-2 + e-2 cos 2t + 3e-24), and L(10e transform as a ratio of two polynomials. b Evaluate L-1 -4* cos ( 3t -) sin ( 4t +)). Express the a s+8 (?(52+16), £² ( s, and L-1 52+4s+5, s++5s3+18s2+34s+20, Solve the initial value problem y" + y" + y' +y = cos 3t with y(0) = 0, y'(0) = 1, and y" (0) = 1 using Laplace transform methods. Solve the initial value problem y" + 3y' + 2y = 2u(t – 2) d with y(0) = 0 and y'(0) = 0 using Laplace transform methods. Plot the solution and the input r(t) = 2u(t – 2) on the same set of axis. Comment on the results. Solve the initial value problem y" + 4y = 8(t – 1) – 8(t – 2n) with y(0) = 1 and y' (0) = 0 using Laplace transform methods. Plot the solution and comment on the results. %3D
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