z is a complex variable, z=x+iy determine which of the following functions u are harmonic. For each harmonic function, find the conjugate harmonic function v and express u+iv as an analytic function of z.      function attached as photo

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

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Q: Find all complex zeros of the function. f(t) = tª – 14,641 .... (Simplify your answer, including any…

A: f(t)=t4-14641

Q: sin z For the function of a complex variable z, the point z = 0 is 3 OA. a pole of order 3 B. a pole…

A: Given that a complex variable function sin(z)/z3 , the find the singularity or pole at z = 0.

Q: zl 5. Trigonometric form of the quotient of = 6cis (2); z2 = 2cis () is:

A: The given quotient of z1=6cis2π3; z2=2cisπ6. Find the value in trigonometric form.

Q: Use the function f and the given real number a to find (f -1)'(a).  f(x) = cos(4x),    0 ≤ x ≤ π/4,…

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Q: Q.1 (a) If f(z)=3z?-6z+3i, find u and v and calculate the value of f at z=2+i. Solution: (b) Verify…

A: For harmonic conjugate we use Cauchy Riemann equation.

Q: Q5 The imaginary part of the complex function f (z) is, v(x, y) == x4 – 6x²y² + y4 (i) Prove that…

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Q: 1. Given a complex valued function can be written as f(2) = w = u(x, y) + iv(x, y), where u is the…

A: The given function is fz=z 1-eiz+z. Substitute z=x+iy   and  z=x-iy in the above function and…

Q: Write a in the form a = a-T+a,N at the given value of t without finding T and N. )3 (7 e*cos t)i+ (7…

A: Given that;                      a(0)  = atT + anN     Let's   Find  the value of at and an.

Q: y + 2xy). Find values of a and b so that f (x + iy) will be analytic. Consider the complex-valued…

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Q: z is a complex variable, z=x+iy determine which of the following functions u are harmonic. For each…

A: Basic definitions and Cauchy Riemann equations.

Q: The function Im(- COS Z ) is harmonic in the C- (0}. ez Select one: O True O False

A: Before the answer of this question we must know about the harmonicity of the real and imaginary part…

Q: a) Prove that f(z) = |z is not harmonic functions but f(z) = In(z) is harmonic. b) Using Demoivre's…

A: This is a problem of complex analysis.

Q: Consider the function f(x) = 4sin(π/2 x) + 2  a. Find the first three positive values of x for…

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Q: A)Determine the value of (-9+j 6) , expressing the result in polar, exponential and rectangular…

A: A) Consider the given complex number, -9+j65 Here we need to find the value of the complex number.…

Q: 2/ A) Prove the identity Sin (A + B) + Sin (A - B) = 2SinA cosB B) Find real numbers x, y, z for the…

A: The trigonometric functions can be proven by using trigonometric identities. The trigonometric…

Q: Let A be a fixed constant positive number and f be an entire function with the proper that If(z)|S…

A: Second option is correct. (az^2+ bz is correct.)

Q: The imaginary part of the complex function f (z) is, v(x, y) == x* –- 6x²y² + y* (i) Prove that v(x,…

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Q: Use the function f and the given real number a to find (f ) (a). (Hìnt: See Example 5. If an answer…

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Q: Consider the following. (V3 + i)(1 + i) (a) Write the trigonometric forms of the complex numbers.…

A: We have to proof

Q: 32. (i) Given that z = e6, show that z" +z-n = 2cos ne. Use this result to express cos 0 in terms of…

A: For 32 part (i) De Moivre's Theorem is used.

Q: Given the complex-valued function 1+z z² Evaluate f (¹) (A) -4-3i (B) - f(z) = (C) −¹+²i (D) none of…

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Q: /2 p2x 1. Evaluate f/²*** cos(x - 2y+z) dydzdx. (Hint: Use the fact the sine is an odd function.)

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Q: Q5 The imaginary part of the complex function f(z) is, v(x,y) = x* – 6x?y? + y* (i) Prove that…

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Q: Comolex unmber analysis Solve the following complex numbers 1.)  sinh[ln(8 + j0)] + cosh(8ej0.785)

A: We have to solve the given complex number sinhln8+0j+cosh8ej0.785

Q: Cos (z) The domain that the function f(z) is analytic function: 23+1 %3D A. C the set of all complex…

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Q: Which one of the following equations has a real root in the interval (0, 2) (A) 3" = sin(x) – 1 (B)…

A: With the help of graph we can easily find out the number of real roots of the given equations.

Q: Eliminate the arbitrary constants in the following equations. Express your answer in its simplest…

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Q: III. Solve the hyperbolic function of the following. 1. Find x in coshx = sinhx + 2sechx. 2. Express…

A: To find x. Some hyperbolic relations are, coshx=ex+e-x2,  sinhx=ex-e-x2,   sechx=2ex+e-x Given…

Q: Show that the following functions are harmonic, that is, that they satisfy Laplace's equation, and…

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Q: Q1: a) Find the 10th power of 3- 2i using De Moiré's theorem and write the answer in the form a +…

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Q: Is the complex function below analytic or not, show that ƒ (²₂) = 2x² + 2y² − y +i (4yx − x) -

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Q: Q5 The imaginary part of the complex function f (z) is, v(x,y) == x* – 6x²y² + y* | (i) Prove that…

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Q: The function Im(- COS Z ) is harmonic in the C-(0). ez Select one: O True O False

A: Answer is : False.

Q: Q5 The imaginary part of the complex function f(z) is, v(x, y) == x* – 6x²y² + y* (i) Prove that…

A: A function u:R2 -> R is harmonic iff uxx + uyy = 0

Q: Q.1 (a) If f(z)=3z?-6z+3i, find u and v and calculate the value of f at z=2+i. Solution: (b) Verify…

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Q: 10. Given the complex function 1+z z² Evaluate f (₁¹) A. 1 + 3i f(z) = B.-1-3i = C. 1-3i D. -1 + 3i…

A: Given that a complex function - f(z) = (1+z)/z. And we find f(1/(1-i)). Here i = "iota" that is an…

Q: Being the one-dimensional eguation a²w a²w at2 Əx² Where w is the height of the wave, x is the…

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Q: Using Cauchy-Riemann equations, we get that f(z) = |z – 3i|2 is O analytic at z=3i differentiable at…

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Q: 17. Identify the equation represented by the graph below: 18. Given the function below, find f(6):…

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Q: EXERCISE State whether or not the following are mathematical statements. In the case of a statement,…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: _1. What are the domains of the function y = 2 cos (x +-)? %3D А. R B. [-2, 2) C. (2, -2) С. D. Q…

A: Answer = (1)  We have to find domain of function  y = 2 cos(x + π/3)

Q: 4. Where are the following functions differentiable? (е) 2z

A: We have to solve given problem:

Q: Classify each singular point (real or complex) of the given equation as regular or irregular. 3x2y"…

A: Given differential equation  3x2y''+6xy'−2xy=0......1 We have to classify the each regular point.…

Q: sin z For the function of a complex variable z, the point z = 0 is A. a pole of order 3 B. a pole of…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: lal-21 Let f (z) = Find the imaginary part of f(z).

A: Given,          fz=z-2iz

Q: Euler's formula: e® = cos(0) + i sin(0) Using Euler's formula, the complex function e 10+12 )t can…

A: To find u(t) and v(t)

Q: un J-2√√2+x (c) Let u₁ = x² - y² and u₂ = x³ - 3xy². Show that u₁ and u₂ are harmonic functions and…

A: Solution

Q: 4-2) Given that z = 2(cos () +jsin ()) satisfies the equation z* = c(1+jv3), where c is real a. Find…

A: De moivers theorem for complex number  (cosθ+isinθ)n=cos(nθ) +isin(nθ)

Q: Find a cofunction with the same value as the given expression. 2n tan ..... The answer is (Simplify…

A: Given, tan2π5 We have to find the cofunction with the same value as tan2π5