Use De Moivre's Theorem to evaluate [-6+ 2i]6

Q: 7. tan(3 + 4i)

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Q: Use Residue theorem to evaluate dx - x2- 8x+ 17 00

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Q: Find Taylor's Sen'ed fey ci) f(x) = sin (2) about x= 1

A: see 2nd step.

Q: Determine a two term expansion for the large roots of x = tan x and rtan x = 1.

A: "According to the guidelines we will solve first question. Kindly repost second question…

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

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Q: Use Residue theorem to evaluate dx x²-8x+ 17 00

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Q: Prove that J1/2 = sinx

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Q: Prove that L (sin² x 2/3 ; p} = 1/ 108 р x (1²,5 + 4)

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

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Q: Find the integrals using complex analysis x' +1

A: "Hey, thanks for the question. Since there are multiple questions posted, we will solve the first…

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

A: We have to express  in terms of a+bi.

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

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Q: tan(2 – j5) j(2-j5) +7- jv2 In(-5)| (3220° – sin 20 + jln5)*|

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Q: Prove that for all whole numbers n ≥ 1,

A: Explanation: Given that,  n≥1dndxnsinx=sinx+nπ2   Formula Used: 1. ddxsinx=cosx 2. ddxcosx=-sinx

Q: Find the last (right) two digits of 77'. use Euler's theorem to solve it

A: We need to find the last two digits of 777. To find the last 2 digits means we need to find the…

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

A: The given complex number is: (- sqrt 3 - i)^6. Let us consider, r cos theta = -sqrt 3 r sin theta =…

Q: 3. Prove that: tan-1z +z %3D

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Q: Provide a complex definite integral that has an answer of 20.

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Q: prove thati- Exi 2. (Exi) 2. (xi-X

A: Solution-: We prove that,

Q: Example Find the root of the equation cos x = xe* using the bisection method prrect to four decimal…

A: Given the equation cos x=xexcos x-xex=0 Suppose fx=cos x-xex We will find the root of the equation…

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

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Q: Use Residue theorem to evaluate cos5x dr x²+1

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

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

A: The given expression is 22+22i20.

Q: Show that given that z = sin-12 дхду дудх

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Q: What is the value of the i in the ex

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Q: 27 do Evaluate the intergal using the residue theorem. 0, 15 + 3 sin 0

A: The given problem is to evaluate the given integral using residue theorem, we have to convert the…

Q: 2 sin 50 do. 9. Use the residues' theorem to evaluate sin o

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Q: do Evaluate the intergal using the 12 + 8 sin 0 residue theorem.

A: The general form of a complex number is given by z=a+ib, where a,b are two real numbers and i=-1.…

Q: Find the last (right) two digits of 77". use Euler's theorem to solve it

A: we have to find the last two digits of 777

Q: Use the fourth Maclaurin polynomial for cosx to approximate cos 12, cos

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Q: evaluate using the appropriate method or combination of methods.

A: We will need by parts method with

Q: Prove that there is a real number r so that sin(r) = x – 1.

A: We have, sinx=x-1 Let us consider a function fx such that, fx=x-1-sinx

Q: Prove the equation sec2 x csc2 x = sec2 x + csc2 x is an identity.

A: Given equation is, sec2csc2x=sec2x+csc2x

Q: Evaluate the integral. 9-sin 4x 4.

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

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

A: Given, 22+i2212  We have to write the answer in the form of a+ib using De Moivre's theorem.

Q: Determine the exact function value of cosh (In 2).

A: The given function is  Cosh(ln2)

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

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Q: apply Residue theorem to find the -2n cos20 do. 3+2sine

A: Use the following formulae, to obtain the solution. Let z=eiθ be a complex number. The real and…

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

A: Given expression is (23+2i)-5 We have to use De Moiver's theorem to simplified the answer in the…

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

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Q: Use the Second Fundamental Theorem of Calculus to evaluate 7. Part of the sin 2x the following…

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Q: lime

A: The epsilon-delta definition of limits:   The limit of f(x) at x = c is L if for any ε>0 there's…

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

A: From the De Moivre's theorem, a+ibn=rncosnθ+isinnθ Where r=a2+b2 and θ=tan-1ba

Q: Prove that cosx = x³ + x< +4x has exactly one root in [0,pi/2]

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Q: Vx3 (х + 5)dx.

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Q: Show that f(2) = (2-1) cos) singue has an essential z + 2 at 2=-2

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

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

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Q: Find the exact value of:

A: Given that, To find the exact value of  sin 7π12 by using the identity, sin ( A + B) = sin A cos B…