2-)The complex function f(z)=u(x,y)+iv(x,y) can be differentiatedat any point in the complex space. The real part of this functionis given as u(*, y) = e¬* [xsin(y) – ycos(y)].a) Show that the u(x,y) function is harmonic.b) Find the imaginary part v(x,y) of the function f(z).c) Determine the derivative of the function f(z) at z=i.

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2-)The complex function f(z)=u(x,y)+iv(x,y) can be differentiated at any point in the complex space. The real part of this function is given as u(*, Y) = e=² [æsin(y) – ycos(y)]_ a) Show that the u(x,y) function is harmonic. b) Find the imaginary part v(x,y) of the function f(z). c) Determine the derivative of the function f(z) at z=i.

2-)The complex function f(z)=u(x,y)+iv(x,y) can be differentiated at any point in the complex space. The real part of this function is given as u(*, Y) = e=² [æsin(y) – ycos(y)]_ a) Show that the u(x,y) function is harmonic. b) Find the imaginary part v(x,y) of the function f(z). c) Determine the derivative of the function f(z) at z=i.

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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Question

2-)The complex function f(z)=u(x,y)+iv(x,y) can be differentiated
at any point in the complex space. The real part of this function
is given as u(*, y) = e¬* [xsin(y) – ycos(y)]
.
a) Show that the u(x,y) function is harmonic.
b) Find the imaginary part v(x,y) of the function f(z).
c) Determine the derivative of the function f(z) at z=i.

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