и (х, у) 3D х3 +х — 3ху? What is the imaginary part of the analytic complex function if(z) = u(x, y) + i v(x, y) whose real part is given above?

Q: If Z1 =1- j3, Z2=-2+ j5 andZ3 =-3- j4, determine in a + jb form: Z1Z2Z3 О а. -5- ј85 О Б. 5+]85 О…

A: We have to multiply the given three complex numbers.

Q: What is the complex variable?

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: for the quartic function represented by this graph?

A: In the given question, the concept of quartic function is applied. Quartic Function A quartic…

Q: Let F = (3z + 3x²) i + (6y + 4z + 4 sin(y²))j + (3x + 4y +6e²² (a) Find curl F. curl F - (b) What…

A: We will use result of part c  which gives line integral in closed curve and combined it with line…

Q: D) Factor f (x) = x³ + 2x2 + 4x +8 into complex linear factors. %3D

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Q: Please solve number 3

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Q: #2. Define the operators 33/32 = 1/2 (3x +²y), 32= 2 (x-7) = u(x, y) +iv(x, y), show that (af (3) =…

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Q: Find the two roots of (j)'/2 in rectangular. a) 0.770 + j0.770, –0.770 – j0.770 c) 0.707 + j0.707, –…

A: c

Q: 6. Show that when 0</z - 11 < 2, Complex Analysis (z-1)" (2-1)(2-3)=-3 (2- #=() 2(z-1)

A: Here we prove this statement by using series expansion.

Q: Function of A Complex Variable Problem Find the image of x² - y² = 1 under the mapping f(z) = N

A: We have to find the image of  under the mapping

Q: B) Find all of the second derivatives for f(x, y) = (3xy2 + 2xy + x²) In; x²+y² itable graph and…

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Q: a) f(z) = vz+Vz - 1 b) f(z) = Vz2 +9 %3D

A: A branch point of an analytic function is a point in the complex plane whose complex argument can be…

Q: The domain of the function f(x,y) =, ху is x² + y? The upper half plane without the origin The…

A: Given function: fx,y=xyx2+y2

Q: (a) S,(Iz – il2 – z) dz along the semicircle y = 1+ et“, 0 < t < n; -

A: ∫γz-i2-zdz=∫0π1+eit-i2-1-eitieitdt=∫0π1+cost2+sint-12-1-eitieitdt=∫0π1+cos2t+2cost+sin2t+1-2sint-1-e…

Q: eiz 5. Evaluate dz, where; (z+2)²(z-1) (a) y is the circle |z| = 1/2 traversed once…

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Q: 2 [11]₁v=₁-1²] W u Compute: u.v= u. W = w u · (v + w) = u.v+u. W =

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r'"(t). 5,3K r(t) = t²i - 4tj + 3. %3D (a) r'(t) (b)…

A: Vector

Q: 1) What are the imaginary roots for the function p(x)= x^4 −8x^2−8x+15? You will likely have to…

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Q: DON'T USE CHATGPT Solve the following equation by canceling operator y"+y = 3x sin(x) (In the answer…

A: First of all we find the auxiliary equation for the corresponding homogenous equation. Find the…

Q: (d) Let Z₁ = −4+ 8i and Z₂ = -1 -2i. Show that (i) 21/2₂ | = 4. | (ii) (iii) |z₁|² +Z₁ Z₂ = 100.…

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Q: Is known f(x,y) = x3y2 = - 426 x3 05 f Determine дугдхдуг

A: Given: fx, y=x3y2-4y6x3To determine ∂5f∂y2∂x∂y2.

Q: T at = 8²T əx² with [B.C] T₂ (0,t)=0, T₂ (2,t) = 0 and [I.C.] 7(x,0)=f(x)

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Q: The domain of the function f (x, y) = y-x2 is A) {(x, y)|x 2 y²,y # F2} B) {(x, y)\y > x², x # +2}…

A: For any function y=f(x) the value for f(x)≥0 for the function to exist. The given function is a two…

Q: 1- DETERMINE A AND BEC FOR THAT THE FUNCTION: (f:C+a=+b -2 +az +b f(=) = IF = #1-i, 2-1+i (f(1– i)…

A: Continuity of complex function:

Q: f(2) = u(x, y) + iv(x, y) 1-) the complex function can be differentiated at every point in complex…

A: In the given question we have to show the the imaginary part of f(z) say v(x,y) is harmonic. and we…

Q: du du dx' dy 1) u = 3x²y + xlny² - Inxy 2) u =xe*Y+ ‡ ArcTan , 3) u = +2²-3² I. Find and (whenever…

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Q: 1 Let f (z) z - 8 Part (a) Integrate the function f (z)along the curve C the complex plane given by…

A: Using the Cauchy integral theorem on the closed contour for part(b).

Q: - 4( Let u(t) = 8t i+ (-9)j-8k and v(t)= e'i+9 ej- e "k. Compute the derivative of the following…

A: topic - dot product and derivative of a function

Q: Integrate f(x, y) = (x + y + 7)-2 over the triangle with vertices (0, 0), (2, 0), and (0,4). (Use…

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Q: #1. ca) perform the operation (1-√32)-10 (6) Find the cubic roots of 1+√3 2. Express your answer in…

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Q: Classify, according to type (hyperbolic, elliptic, parabolic) the equations (i) Uxx +2Uxy +Uyy −Ux…

A: Let the partial differential equation be AUxx + BUxy + CUyy + DUx + EUy + F = 0 If B2−4AC&lt;0, then…

Q: II. Use Cauchy – Reimann Equations to identify if it is differentiable or not, if yes then…

A: To answer the given question we shall use the following Proposition- Proposition: If f=u+jv , fx and…

Q: Find the value. 11) If F(x, y) = -9x+4y, find Fx(-4,-9) and Fy(-4,-4), xy A) Ex(-4,-9) = 1,…

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Q: Calculate the imaginary part of  ∮C(Re(z)+3.43)(1z^2+9z+11 / z)dz  where C:|z|=1  Use FOUR…

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