Cauchy-RiemannConsider the complex function of a complex variablef(z) = (z*)²,where z* is the complex conjugate of z = x + i y. Show thatf(z+Az)-f(z)ΔΖf'(z) = limAz-0depends on the direction of Az in the complex plane, and, so, f'(z) is not well-defined.

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Answered: Consider the complex function of a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Consider the complex function of a complex variable f(z) = (z*)², where z* is the complex conjugate of z = x + i y. Show that f(z+Az)-f(z) Δz f'(z) = lim Az-0 depends on the direction of Az in the complex plane, and, so, f'(z) is not well-defined.

Consider the complex function of a complex variable f(z) = (z)², where z is the complex conjugate of z = x + i y. Show that f(z+Az)-f(z) Δz f'(z) = lim Az-0 depends on the direction of Az in the complex plane, and, so, f'(z) is not well-defined.