I. Solve using De Moivre's Theorem. 1. Find all the value of x so that x4 = -8(i – V3) z-1 2. Given that z is not real number and |z|= 1, show that w = z+1

Q: (b) For what value of u have the following homogenous equations non trivial solutions? . (1 – µ)X1 +…

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Q: Using De Moivre's Theorem, solve the following; z5 = 1– 2i

A: We have to find the roots of complex number.

Q: 3. For what values of to and ro does the IVP: x' = 2/r, x(t.) = xo, have a unique solution?

A: Given: The initial value problem x'=2x, xt0=x0

Q: Given that z ∈ C where |z| = 1 , solve for : |1 + z|2 + |1 - z|2

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Q: Q.4 Solve Cauchy Euler DE x³y" + 4x²y" – 5xy' – 15y = x*

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Q: George is standing in front of a silo and can only see as far as the diagram shows. Determine the…

A: By two-tangent theorem,tangents which meet at the same point are equal in length

Q: Solve the following equation, working over Z20 and over Z respectively: a2 + 5y? 322.

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Q: A) Find the values of x and y that satisfy the equation: In(3 + j4) +7+1²2= j(x − y) + (4x + j2)…

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Q: 7. Prove (by writing the linear algebraic equations explicitly) that (a) If x-y=0, then =ỷ where X,ỷ…

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Q: Determine the general solution of the second order "Euler equation" and specify the interval in…

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Q: We are also given that eRd, where is that in the solution?

A: The previous answer is not correct....See this answer

Q: Consider the DE: x' -[2, x, with solutions x = and x2 = 12 a) Verify that x, and x, are solutions to…

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Q: Given that ZEIF = LGIF, prove that FH 1 EG. E H. Begin by listing all the facts you know for this…

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Q: The Crank-Nicolson method used to solve parabolic PDES is stable for O a. As 1/2 O b. Az 1/2 Oc all…

A: In the question it is asked to solve for parabolic PDEs.

Q: (a) Use the Intermediate Theorem to prove that Vx + Vx + 7 = 3 has a solution in the interval [0,…

A: We have to use intermediate value theorem.

Q: Use Gauss- Jordan to solve the values of x,y and z for this problem: 2x – y+z =-3 x+y-z = 6 3x - y-…

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Q: Use separation of variables to find a family of solutions to the following PDE и (т, t) — с'и (т,t)…

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Q: . If g (t) = d, where d is a Real number, show that every solution approaches as t → 0 .

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Q: дz For z = x² + xy³; x = uv² + w², y = u + vew, find when u = 2, v = 1, and w=0 dv

A: Let's solve given derivative functions.

Q: Use the intermeiate value theorem to show that the following equations has at least two distinct…

A: Solved below

Q: 1. Prove that C(n, r) = n!/r!(n – r)!

A: Since you have asked multiple questions we will solve the first question for you. If you want to be…

Q: а — 5 x +1 7+За 2ах — 5 х — 2 ? — х — 2

A: a-5x+1-7+3ax-2=2ax-5x2-x-2 Now, simplify the above equation.…

Q: Find all solutions for x, showing all work. (Vx - 9)2 - 7(x - 9) + 10 = 0 %3D |

A: We have to find all solutions for x for the equation…

Q: Which statement is true about the equation r(x) = 9 (x) given r(x) = 2x + 3 and 9(x) = x²? O A. It…

A: Here the given functions are                                        f(x)=2x+3…

Q: Using a suitable substitution, solve z* + 3z2 – 28 = 0, qu x lo 219wog - (ahem A) where z E C

A: Given equation is        z4+3z2-28=0 , z∈ℂ We will solve this equation by suitable substitution.

Q: Solve the following Cauchy problem: -00 0, u(r,0) =r-r, (x,0) 4r, -x <r<x.

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Q: ABCD is a rectangle. A В 4 3 1 E 5 Given: mz1 = (4x – 28)° mz2 = (x + 12)° - Solve for x. m23…

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Q: Given that P(z-M)-0 wherei(1LO(1-20andP and Q are real constants. Write down in a form a+bi and find…

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Q: Consider the equation -u" + qu 0 and suppose qo ≤ = q(x) ≤ 9₁ < 0. Show that for two consecutive…

A: The solution is hand written as requested:

Q: A solution to the DE ydx-xdy=0 is A B C D xy=C x = Cy none of these x=y=C

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Q: 4. Let X e R"×m Show that XTX > 0. nx

A: Note: Since we are not allowed to provide you a handwritten solution, we have provided you a typed…

Q: (1– (C+D)), provided (C+D) 4PQ. (28) Substituting (25) and (26) into (28), we get the condition…

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Q: Suppose z-2z +x=5, What is the value of y ? | - 3 3 0 3i nim

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Q: What values of α and A make y=Acos⁡αt a solution to y″+2y=0 such that y′(1)=3? α= A=

A: We have to find value of a and A.

Q: What values of α and A make y=Acos(αt) a solution to y′′+6y=0 such that y′(1)=2?

A: The solution of differential equation y’’+6y=0 is

Q: Given that 212-y? - 2r c is a one-parameter family of solutions of the DE dy = 2r - 1, dr %3D find…

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Q: A. If:Z = x + iy, Solve the following equation to find x and y: 4x+ y_ 4y+14 -0 then use Demoivre's…

A: Given: - If Z=x+iy and the equation is, 4x+y1+ix-4y+i4iy=0 To find: -The value of x and y. Then use…

Q: 1) Rewrite c(r) = 2+5z+2 I-3 in the form y= q(x) + He where r has degree less than b.

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: (e) Is there some b € R' for which the equation Ax b has a unique solution x? (Explain briefly.)

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Use undetermined coefficients metho to find the generel solution to the given DES - (3) (c) j +4y'=…

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Q: 2. Verify that r = Cie +C2 is a solution to a" – r' = 0. Find C1 and C2 so that r satisfies x(0) = 1…

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Q: Find all possible pairs of integers x, y so that 7x + 3y = 4. Then find which of these pairs makes…

A: Given:   7x+3y=4                        ........(1) We have to find all possible pairs of integers…

Q: B. Prove that the given equation is a solution to the given DE: 7. y = Ax + Be* ; (x- 1) y" - xy' +…

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Q: Solve the following equation uxx + Uyy = 3x - 5y with the conditions for the square plate u(0,y)=0…

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Q: Solve the following DEs: 1. 4y" + 16y' + 17y = 0, when y = 1, x = 0; y = 0, x = n

A: Note: As per bartleby instruction when more than one question is given only one has to be answered.…

Q: - ydx+ (x+ /xy kdy = 0 (Homogenous)

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Q: Show that the following equations have at least one solution in the given intervals, rcos t 2x² +…

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Q: 20. Find the constants xo, X1, and c so that the quadrature formula f (x) dx - 2 x) +cif(x) has the…

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Q: The Crank-Nicolson method used to solve parabolic PDES is stable for a. A# 1/2 O b. all values of A…

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