Verify that the given complex function is an Analytic Function, w = f(z) = 2z³ – 2z + 12

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Q: Verify that the given complex function is an Analytic Function, w = f(z) = z³ + z + 12 %3D %3D

A: Given that:

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Q: Assume that 1<a<b and a/x+ x = 1 /(x - b) . Show that this equation is solvable.

A: Given that the equation, To solve the equation,

Q: Verify that the given complex function is an Analytic Function. w = f(z) = 2z³ – 2z + 12

A: To verify: Given function is analytic.

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Q: Enter the function In standard form. y = 2(x-1)(x +5) The standard fom of y = 2(x-1)(x +5) is

A: y=2(x-1)(x+5) first multiply (x-1)(x+5) =>(x-1)(x+5) =>(x^2 +5x -x -5) =>(x^2 +4x-5)

Q: find the linearization at x = a. f (x) = x4, a = 1

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Q: Verify that u(x, y) = x² + 4x – y² + 2y is harmonic and find %3D - a) the harmonic conjugate…

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Q: и (х, у) 3D х3 +х — 3ху? What is the imaginary part of the analytic complex function if(z) = u(x, y)…

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Q: (4)Find the scalar function such that F = V ø y i+ where F=- *+y x+y

A: We can find scalar function ϕ such that F→=∇ϕ ;where ∇ =i^∂∂x+j^∂∂y+k^∂∂z

Q: Q1 Verify that the given complex function is an Analytic Function, w = f(z) = 2z³ – 2z + 12

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Q: The imaginary part of z=x+iy is x

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Q: Q1 Verify that the given complex function is an Analytic Function, w = f(z) = 2z3 – 2z + 12 %3D

A: Given that, w=f(z)=2z3-2z+12 Now, put w=x+iy…