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1 )2 + ơ-2)2] is harmonic in every region which does not include the point (1,2).(a) Prove that ψ = Inf(x-(b) Find a function ф such that ф + ir is analytic. (c) Express ф+3.54.as a function of z.

Question

Question attached. Z is a complex variable, z=x+iy 

1 )2 + ơ-2)2] is harmonic in every region which does not include the point (1,2).
(a) Prove that ψ = Inf(x-
(b) Find a function ф such that ф + ir is analytic. (c) Express ф+
3.54.
as a function of z.
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1 )2 + ơ-2)2] is harmonic in every region which does not include the point (1,2). (a) Prove that ψ = Inf(x- (b) Find a function ф such that ф + ir is analytic. (c) Express ф+ 3.54. as a function of z.

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Step 1

To verify the Laplace equation (harmonicity condition ) for the given function and to find its harmonic conjugate

Step 2

A real function V(x,y) is said to be harmonic if V satisfies the Laplace equation: (here subscripts denote partial derivatives) 

Vxx+Vyy=0

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Step 3

Let us verify that the given fun...

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