Suppose z = (7) + (4)i. Then Im (z ') =?

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Q: Q1. Let f = u + iv and f(z) = z. Prove that u and v satisfy Laplace's equation.

A: I have find the U and V first then the laplacian of that.

Q: 2 = 1+ 2i 2- i and w = what is z + 3w ? a. 7+i C. 5+ i b. 7-i d. 5-i

A: Solution

Q: The Joukowski map is defined by

A: Given, the Joukowski map is defined by                                     w=f(z)=12z+1zTo prove…

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Q: 4. Use the inequality | sin r|< |x| for x E R to show that the sine function is continuous at r = 0.…

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Q: 1) Let p: R* → R be a linear transformation such that: p:(1,0,0,0) = 1, p(1,–1,0,0) = 0,p(1,–1,1,0)…

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Q: Problem 2: Let T : R³ → R² be a linear transformation such that T(e1) = (1,3), T(e2) = (4, –7), and…

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Q: (b). Show that iff= u+iv is analytic in a region S and u is a constant function (i.e., independent…

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Q: and its der Foo the Fin d function f(z) = | - K i+ 2+eZ %3D

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Q: Suppose f has a zero of order k at zo. Show that ‹ƒ′(²). f(z); ²0) = k. Res( (Hint: Express ƒ(z) =…

A: f has a zero of order k at z0 We have to prove Resf'zfz;z0=k

Q: Find Radius of converges to the series =0 -) zn

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Q: 1337 i+1` Compute ()

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Q: Problem 2. Consider a set of polynomials {p1(t),..., Pm(t)} in P, with p:(t) .+ a t" for i = 1, ...,…

A: Note: There is a typo of m and n in the given question that we modified here and marked bold.…

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A: Given: Indirect method of proof : given if A is true then B is true.

Q: True or false (Provide/Show Justification for answers) (a) f (z) = |z|² is differentiable at zero?…

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Q: Write the first and second partial derivatives. g(r, t) = t In r + 13rt7 - 4(9) - tr gr = 9rr = 9rt…

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Q: Problem 2. Let p be a real number such that 1 0, and the function Tf is continuous on 10, ∞[ and…

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Q: 4.) Let f(z) be an analytic function. Show that the following equality is hold. %3D

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Q: 1:1:2•: 3:1:4:|'5|:6:1:7:1:8.1 9.1 10: I 11: |·12: | •13• T 14: 1·15: |·16· I 17. I 18. | • 19:…

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Q: Trace O P and point A. Construct a tangent to O P that passes through A.

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Q: Let f (2) = 2² + 71m (2). If f(2)= u(x,y) + iv (x,y), find u(x,y) C. 2xy-y² A. x² + xy-y² D. xy-y²…

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