a) Find an analytic function (or functions) if 2 Ref(Z) = x ² = y ²² + 2 x and fli) = 2i - 1 b) Find all the analytic functions for which Rez = Im f(z)

Q: Show that the function is harmonic and analytic w=3Z² + 4iZ

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Q: 1+х f[X_, Y_] := 2 у - 1-x (1+) (у-1)2

A: We will use basic knowledge of the functions of several variable theory to answer this question.  We…

Q: Simplify and find for each of the following functions without using product rule and dy dx DENT…

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Q: „Show that the complex variable function below is differentiable analytic only at origin point? f(z)…

A: We will show the required result.

Q: Find all the analytic functions for ReZ=Im f(z)

A: Find all the analytic functions for ReZ=Im f(z)

Q: Examine whether the following function is Analytic or not ¹() (z) = ln(x² + y²) + i tan-¹

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Q: Q2/Show that the functions is harmonic u = 2 x (1 - y)

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Q: Find an analystic function whose real part is e-x (x sin y-y cos y)

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Q: (3 lin X > otleax

A: Solving limit

Q: a) Find an analytic function (or functions) if Ref(z) = x² - y² + 2x and fli) = 2i - 1 b) Find all…

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Q: We can not find an analytic function f=u+vi such that 3u-v is not harmonic. * True False

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Q: of For the function f(x.y) = In (x + 6y), find- of and dy

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Q: Discuss the analyticity of  f(z) = Re(z 3)   Find whether the given function is analytic or not.…

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Q: Prove that dl = (Vu) x (Vv) - do.

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Q: Oz(-@) and Ør(@) are conjugate functions. That is, Px(-@) =Øx°(@) %3D and Oz"(-@) = , (@)

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Q: Show that xy² cannot be real part of an analytic function.

A: Real part and Imaginary part of  analytic function is satisfying the harmonic.

Q: Find an analytic function whose real part is e-x(x sin y-y cos y )

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Q: Determine the values of a and b such that the function is differentiable on (-, x2 +b, x〉2

A: Given piecewise function is:A function is differentiable when it is continuous and the left and…

Q: 1. Use the Power Rule and properties of derivatives to find the derivative of each function a) f(x)…

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Q: Prove that the function n = x(x^2 - 3y ^2)+ (x^2 - y^2) + 2xy is harmonic. Also find the conjugate…

A: Then,     and Thus,   and , it follows  that .Hence, the  given function is harmonic.(Proved)…