Which of the following functions of the complex variable z = x+iy = ret0 are analyticand which ones are not analytic?(i) f(2) = x² – y?(ii) f(2) = x² +2ixy - y?(iii) f(2)= x² + iy?(iv) f(2) = i0 + lnr(v) f(2) = r²(cos 0+i sin 0)(vi) f(z) = rªeia®, where a is some real number.Calculate df /dz for the analytic functions , and of/az for the rest of them.Find the analytic functionw(z) = u(x, y) +iv(x, y)if (a) u(x, y) =x³ – 3xy², (b) v(x, y) = e-" sin x.| Exercises

Which of the following functions of the complex variable z = r+iy = ret0 are analytic and which ones are not analytic? (i) f(2) = x² – y? (ii) f(2) = x² + 2ixy-y? (iii) f(2) = x² + iy? %3D %3D %3D

Which of the following functions of the complex variable z = r+iy = ret0 are analytic and which ones are not analytic? (i) f(2) = x² – y? (ii) f(2) = x² + 2ixy-y? (iii) f(2) = x² + iy? %3D %3D %3D

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter4: Nonlinear Oscillations And Chaos

Section: Chapter Questions

Problem 4.14P

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Question

Which of the following functions of the complex variable z = x+iy = ret0 are analytic
and which ones are not analytic?
(i) f(2) = x² – y?
(ii) f(2) = x² +2ixy - y?
(iii) f(2)= x² + iy?
(iv) f(2) = i0 + lnr
(v) f(2) = r²(cos 0+i sin 0)
(vi) f(z) = rªeia®, where a is some real number.
Calculate df /dz for the analytic functions , and of/az for the rest of them.
Find the analytic function
w(z) = u(x, y) +iv(x, y)
if (a) u(x, y) =x³ – 3xy², (b) v(x, y) = e-" sin x.
| Exercises

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