Use De Moivre's theorem to find the following: 4 i. [1+ v3i]" -3 ii. [-1+ v3 i]

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: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

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Q: e*, when 20 = -1 %3D P„(x) sin(nrx) – nn cos(nax), when 2, = (nx)² for n = 1,2,3,.... a.) Show that…

A: Hi! As the questions are lengthy, we are answering only the first subpart. If you need an answer to…

Q: Use symmetry to evaluate the followingintegrals.

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Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approxim

A: Given,         f(x, y)=11-2x-y

Q: If x=sin@,y=0 ,y=cosp0,Prove that (1-x²)y,-xy,+p°y=0

A: Given, x=sinθy=cospθ Required to prove, 1-x2y2-xy1+p2y=0...1 Then finding dydx by using chain rule,…

Q: Find all angles between 0 and 2n satisfying the condition V2 COS T = Separate your answers with…

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Q: show that r = cos 2θ is symmetrical with respect to the horizontal axis.

A: show that r = cos 2θ is symmetrical with respect to the horizontal axis.

Q: 3. Use the theorem in Sec. 48 to show that (z – zo)"- dz = 0 (n = ±1, ±2, ...) when Co is any closed…

A: The given question is solved below.

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

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Q: Use Picard's theorem, find the largest interval for which the IVP (x2+3x-4)y"-tan(r)y'+e*y=7,…

A: Given: (x2+3x-4)y'''-tan(x)y'+exy=7, y(-1)=1

Q: Which integral computes the circumference of the ellipse +y? = 1? 2 216-322 16 – 4x2 dx 16 — З2? -…

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Q: Find all angles between 0 and 2T satisfying the condition COS X = 2 Separate your answers with…

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Q: make the given substitutions to evaluate the indefiniteintegrals. ∫sec 2t tan 2t dt, u = 2t

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Q: Find the extremum of f(x,y) = 9x2y² +4y² + 4x². %3D Answer:

A: Topic= Derivative the extremum is 0.

Q: Given that 3x - tan y = 4, what is dy in terms of y? A 3sin y

A: I have provided solution in step2

Q: Find the length of are リ-Jx-2+ Sa'z) + Sin

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Q: as Let ĝ +sinh (z?) - ji = 27 where w=f (x,y,2)- %3D Find 2 nd JW and au

A: In the given question we have to find the partial derivatives of with respect to x ,y and z. here we…

Q: Find the residues of sin(2²) at z = 0 and z = π. (sin z)2

A: To find the residue of sinz2sinz2 at z=0 and z=π Let  fz=sinz2sinz2=sinz2csc2z…

Q: has at least one solu Prove that the equation r+ sin(x) = VI +3 %3D (0, т).

A: Here we have to prove that,  x+sinx=1x+3⇒f(x)=1x+3-x-sinx has at least one solution in the interval…

Q: Express the following to rectangular form. 1. z = v17(cos346° + isin346°)

A: Rectangular form of complex number is defined as z=x+iy Now simplify the given complex number to…

Q: A force of F(x)=x2−cos(3x)+2, x is in meters, acts on an object. What is the work required to move…

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Q: Fird the Aren of the Reyion c2-9 cos In teriur of (2€)

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Q: Using the substitution z = tan 0, evaluate dz, V81 + 4z²

A: The given integration is: ∫181+4x2dx  To evaluate the given integration.

Q: By the samc way, prove that g 7 sinw.k MUIS Z N-27 cesW. +1

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Q: 2t k, then the distance traveled over 0Sts In 3 is:

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Q: H.W : Use the Trapezoidal Rule with n=6 to approximate. Here f(x)=sin2x,23D0,b=r.

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Q: Let / = x tan(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

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Q: If r(t) = (V10 – t, In(t – 1), sin(2t)) , then the domain of r is

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Q: Find the length of the curve [x = eª cos(t) y = et sin(t) for 04 (Hint: You can simplify the…

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Q: nd the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form…

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Q: Determine the natural cubic spline that interpolates the data f(0) = 0, f(1) = 1, f(3) = 4 %3D and…

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Q: Use the method e muiti plíers of Lagrange to fird the mini mum Value of f(^ig) = x*+4y²-22+8y…

A: Given that: fx,y=x2+4y2-2x+8yg(x,y)=x+2y=7

Q: -8. AB is tangent to to OC at point B. E 6. MZCDA - 8. MZDBA = 32

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Q: Given a level suface 4x2y2 + 3xy = 5 with y = y(x). Find at the point (2, 4). Give your answer…

A: Given surface is: 4x2y2+3xy=5

Q: 2. %3D be Centered in a batt co,ogo) andradies I 2. frove thet S-273R

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Q: ) a) Eliminate the parameter to obtain to obtain an equation in Xandy 5 describe the carve…

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Q: Find the function r that satisfies the given condition. r'(t) = (5, sin 8t, sec ct); r(0) = (3,3,3)…

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Q: Selve the boundaly value preblem (D+ 36)g = and y'(o) = 2 that yte=I Sin 6x, given %3D

A: We know, 1D2+a2sin ax = x2∫sin ax dx

Q: TL 3. sin²4ycos²2ydy T

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Q: Given, a(x,y,2) = 23x3 tan (y) + x*29 %3D Find the expression for Izyz and Caleulate it at the point…

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Q: Find the Võlumé of thé šólid generated by revolving the shaded region about the given axi About the…

A: Explanation: If we rotate the shaded region about the x-axis, we will get the cone shape. Height of…

Q: y = In(1 – a²) ; 0 < æs

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Q: Find the solution by separating variables. Utt = 4uxx (u (0, t) 3D и(2,t) 3D 0 u(x,0) = sin³(,) for…

A: Given a hyperbolic equation, utt=4uxx with initial and boundary conditions as follows,…

Q: please solve this question

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