Find the imaginary component of In(z + w) if z = 16 + 6i and w=7+8i . Round off your final answer in five decimal places.

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A: Suppose any linear differential equation can be written in the form of  dydx=fyx then it is a…

Q: Suppose z = x + 2i and u= 3+ yi where x, y E R. Find the smallest positive value of x z + u for…

A: Substituting z=x+2i and u=3+yi in z+uz-u:  z+uz-u=x+2i+3+yix+2i-3+yi           =x+3+2+yix-3+2-yi

Q: : Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x +2y-z = 4

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Q: The roots of the characteristic equation of (D2 – D+ Dy are A1 = 3 + 4i and A2 = 3 - 4i . 25 15 10 4…

A: We will find the value of the unknowns.

Q: Given that the characteristic equation has the following roots , what is the complementary solution?…

A: Given are the roots of a characteristic equation    1±3i,1±3i⏟,  2,2,2,2,4⏟       Repeated…

Q: Find the value(s) of z which satisfies the equation |z| 2 + 1 + 6i = 6z

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Q: Find the general solution to the given Euler equation. Assume x > 0 4x2y" + y = 0

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Q: Show that the following gn are harmonic and find its conjugate u=3x^2y+2x^2_y^3_2y^2

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Q: find the general solution to the given Euler equation.Assume x > 0 throughout. 16x2y'' - 8xy' +…

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Q: Exercise 3: Solve the following equation for x and y where 3 xy – 2i + x + 2xyi – 5 = -- 3i 2

A: Solution of the equation

Q: the solution of the homogenous equation (хусот х -)dy - Ydx = o

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Q: The approximation of f, xin(x + 3) dx using two points Gaussian quadrature formula is:

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Q: Find a general solution of the equation: 5xy' = 2 – y %3D

A: Please find attachment for the details solution

Q: Z2 in H = {0,4,8} find all left cosettes

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Q: ?The Third Equation for i3 7in+12i3-=-3-O 5i1+12i3=0- Zir-4i2+16i3=-3- 0

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Q: Perform a rotation of axes to eliminate the xy-term. (Use x2 and y2 for the rotated co 3x² - 2√3xy +…

A: Given problem:- Perform a rotation of axes to eliminate the xy-term. (Use x2 and y2 for the rotated…

Q: Show that ePt cos qt and ePt sin qt are linearly independent.

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Q: Verify that x and x* are solutions to x²y" – 6xy' + 12y on (0, 0), and give the general solution to…

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Q: Suppose that f(t) = e (1−2i)t is a complex solution for an unknown second-order linear equation…

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Q: Consider 7(t) = (2t³ – 2, 3e“, – 2 sin(3t)). Find Don't include the +C. %3D

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Q: The roots of a d.e are -1, 2tV3i What is the solution? O a. y = e*(c, cos 3x + c2 sin 3x) + c3 cos x…

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Q: The solve of the equation: In(z+ j)= ja / 6 Is 1 + j 2 2 ||

A: Given:           So,               ln(z+j)=π6j⇒z+j=eπ6j⇒z+j=cosπ6+j sinπ6⇒z+j=32+12j⇒z=32-12j So, it…

Q: Determine the reduced row echelon form of cos e sin e A = sin 0 cos e

A: Given, A=cos θsin θ-sin θcos θ

Q: 18 In(z – 3) Question 10) Find I = -dz, where C = Iz - 2 + 4i| = 4, Ccw z2 + (4 + 4i)z + 3+ 4i

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Q: Solve for the orthogonal traectories y2= 4x²(1- kx) %3D

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Q: 3. Find the general solutions of, x+y dx x-y, a.

A: We have to solve the given differential equation.

Q: Convert the ! √ √4-1² 2 0 following to rectangular 32 r³z² sino cos o dz dv do dz dx dy

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 2 11 3. x*y" – 5xy'+9y= 2x

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Q: Write down all of the product solutions satisfying: и +иу —D 0, 0 <x<2, 0<у<1. %3D u(х,0) — 0, и,…

A: Note:- As per our guidelines, We’ll answer the first question since the exact one wasn’t specified.…

Q: 3x'y"+2xy' = 0 %3D

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Q: Reduce the following equation to a canonical form and hence solve it: 3u +10u xy +3u vy = 0 xXx ху…

A: See the solution in the given fig.

Q: Find the general equation solution to the 2Zx + Zy +Z = o

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Q: a) f(z) = 14/(z2 + 2z + 2) is a complex function, find (1/Tt) S-00° 14/(x²+ 2x + 2)dx

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Q: Transform to normal form and solve (showing the details!) 41. uzz + 2uzy + Uyy = 0

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Q: Exercise 3: Solve the following equation for x and y where 3 xy – 2i + x + 2xyi – 5 =- 3i | 2

A: This kind of problem we can solve by comparing the real and imaginary parts and after that solve the…

Q: find the genral solution (D +2D,D, -2D, +2)u = 0

A: Given  Dx2+2DxDy-2Dy+2u=0   …………………(1) Consider the equation F(Dx,Dy)u=0 Here F(Dx,Dy) =…

Q: Verify that z 2 + 4i is a solution of z2 + 6z - 40i = 0. Is 2+ 41 also a solution?

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Q: dy 1. dr + 3y = 2xe -3z %3D

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

Q: Evaluate the complex integral e19.1.png rx+yi dz az + b if a = 2, b = 6, c= 17, x = 1, and y = 6.…

A: Given  a= 2 ,b=6 ,c= 17  x= 1 and y=6 x+iy= 1+6i

Q: Find the general solution of the following ODOS: (а) x2y"-Зху'+4у3D0, х>0.

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Q: Determine whether y = e', y, = sin2t, ya= cos2t make up a fundamental set of solutions by finding…

A: The Wronskian matrix is constructed using y1 , y2 , y3 and their derivatives. If the determinant of…

Q: Find the solution of the Euler-Cauchy equation x?y" + 0.6xy' + 16.04y = 0.

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Q: Find the general solution to the given Euler equation. Assume x &gt; 0 9x2y" + 15xy' + y = 0

A: Solution:- The given differential equation is  9x2y''+15xy'+y=0..........(1)

Q: utilize the characteristic equations method to solve the equation y''-5y'+3y=0 y(0)=3, y'(0)=-1

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Q: 3x?y" + 2xy' = 05 21"

A: Differential equation

Q: Enter the first few coefficients: az -1/3 = a6 = %3D by=

A: Let, the series  solution of the given equation  d2ydx2+2xy=0......1 be  y=∑n=0∞anxn............2

Q: Now consider the fourth-order equation Yk+4 + Yk = 0. (4.76) Its characteristic equation is (n² +…

A: Differential equation is given, we have to find the determine step.

Q: Explain why an equation Ax = b has a solution if and only if b is orthogonal to all solutions of the…

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