10 2. Use De Moivre's theorem to determine 1 in the form a + ib. 2

Q: 10. Since fis holomorphic everywhere except at z = -lit is known that it maps infinitesimal circles…

A: Given fz=z-1z+1. Then f is holomorphic everywhere except -1. Let z=-1+14i. Then,…

Q: Theorem 23. If u, v E Q then we can find integers a, b, d with d > 0 such that u = a and v = d'…

A: By Division Algorithm we know that,               Let a, b be two integers with b>0. Then there…

Q: 86. Show that Z, = r(cose + isine) and Z2 = r[cos(-6) + isin(-6)] are conjugates. %3!

A: Given,

Q: coprime

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Q: X sec10 can 1. Let u = 7 In х2 - 1

A: Given: ∫x sec107ln2x2 - 13tan7ln2x2 - 13dxx2 - 1.

Q: 15) Find The natural domain (a) fx) =3 os X 6 g0) = ©dix) = Sin? x O ra) = 19-x2.

A: given(a)f(x)=3cosxdomain of this function is (-∞,∞)(b)g(x)=13+xx≥0therefore domain is [0,∞)

Q: The Fibonacci numbers 1, 1, 2, 3, 5, 8, 13.. are defined by the recursion formula xn+1 = Xn + xn-1,…

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Q: 2. Let a € R and n € Z0. Show that of the numbers a, 2a, distance from an integer is at most 1/n.…

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

Q: Use De moivres theorem to determine (3-4))"C4cis 30° )ieave your answer in 10 CiS the Formof Fciso

A: According to the given information it is required to determine the value of

Q: 30. Use the graphic below to answer the question. -7 5 4 -3 2 -8-7-6-5-4-3-2-1, 1234567 8 F3 -5…

A: W = (-3,1) and W' = (-3,-1) Z = (2,1) and Z' = (2,-1)  W and Z are transformed by moving coordinates…

Q: 11. What theorem is used to prove that BD 1 AC? C В. D A

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Q: 2.3 Use the Cauchy integral formulae to evaluate 22 - 1 Jo (9 – 2*)(2 + 2i))" where C is a circle |2…

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Q: Prove that Zo is not isomorphic to Z 10 12

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Q: 4. Prove that C, = ,C4 (Hint: Algebraically show that the Left Side = Right Side)

A: We know that  Cr n= Crn = Crn = (n)!(r)! × (n-r)!

Q: Q4: 1- Prove that (1-0+(1+ () 0. 2. Put in the form a+ib ((1+i))- ((1-i)).

A: Here we have to prove that, 1) 1-i2+(1+i)2=0 2) Put in the form of a+ib, 1+i22-1-i22

Q: 8. Work out a Gaussian quadrature formula of the form Ans. A; = 1, x; = Aif(x1) + Arf (x2). f(x) dr

A: The given problem is to prove the following integral, the proof is to show the 2 point gaussian…

Q: 3. Prove that ur2 +S is irrational. (Hint you may Use the Theorem y.71 which states that ve is…

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Q: 2 2 22 if== prove that 22 a¯x +b¯y¯ +c¯=¯ 3, ,3, 3 a'x + b°y +c°z xyz abc %3D

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Q: By using Caushy Rieman prove that (2) and (3) (2) 4c2) = (3) prove That (3)- 3.

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Q: [1E q14] Question is attached, Thanks ?

A: From the given information it is needed to prove that:

Q: 13. Find another representation 2, in which 3 a. ris negative and 0 < 0 < 2T; b. ris positive and…

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Q: PROVE that 2a + b = 0.

A:

Q: Given that 22 = Z4, prove that Zl= 23. 1/2 3 st at least three facts you may use to complete this…

A:

Q: 13 3. Use the IVT to prove that y = r Inr has at least one zero on 2 2

A: Above function is continuous function in given interval. So we can apply IVT

Q: 4. Let z = -4 + 3i and zw = -7 - 2i. By showing clear steps, find w in the form of | | a+bi.

A:

Q: 1. State and prove the full version of the Pythagorean Theorem

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Q: 9) Use De Moivre's theorem to write 80°)7 m atbi form are exact values, [3 (os 80°+ ī sim 80°)7°…

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Q: Suppose a + bi ∈ Z[i] and c ∈ Z.Under what conditions is it true that c|(a+bi) (in Z[i])? Give…

A: Given that,

Q: Construct a paragraph proof to prove the following: Given: y +2 = (x- 10) Prove: y =x-8

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Q: Find the rank and nullity of the 2. 4 9. A z -7 2. -5 4 L7 -9 2 -4 verify the that dimension…

A: The given matrix is  A=20464-7201-5247-92-4 According to dimension theorem for any matrix A of size…

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

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Q: Theorem 4.8.1 Irrationality of V2 V2 is irrational.

A: For any integer n such that n² is even then n is also even.

Q: 10. Which theorem can you prove, given that mzl=m2 in the figure above? Explain your answer.

A:

Q: What is the midpoint between z1 = 9i and z2 = 4? (2, 4.5) (-4,-9) (-2,-4.5) (4, 9)

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Q: Question is attached, Thankyou

A: Let us take z = x + iy.

Q: 4. Assuming that gcd(a, b) = 1, prove the following: (a) gcd(a +b, a – b) = 1 or 2. %3D %3D

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 2. Solve for the complex mumber z in r (4+ 36) – 7 = 7x - 4zi. Show all algebra.

A: Given expression is x(4 + 3i) - 7 = 7x - 4xi

Q: 8. Determine whether v(x) = r'+3|x| even, odd or neither. Discuss its symmetry.

A: Q8) Given: v(x)=x3+3x

Q: 5 +1 Tsimplify denomina 7) (1+i) (1-1) = 4 the Following without using the de noctor Prove that

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Q: #1 and #2, write a 2-column proof. Given: 5(2x - 8) = 30; Prove: x = 7 %3D 5C2x-8)3D30 Gioen

A: topic:-simplification

Q: (2.5) Find another representation in which a. r is negative and °<0 < 2n. b. ris positive and -2n <0…

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Q: 7.1) 19) Evaluate the integral.

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Q: 1. (a) Let 5 -6 -6 B = |-1 4 2 3 -6 -4 Find oigon nigon un imil to D

A: To finding the eigenvalues and eigenvectors to the given matrix we use Gaussian elimination method.…

Q: If z=2e(i pi/20), use De Moivre's theorem to compute z5

A: Use demoivre theorem

Q: (a)] Show that 1+(1+z)/2 csch z In • [(b)] Use part (a) to find all the values of csch (-2i).

A: Let:

Q: 4. Verify thatf (x) = x³ – x2 – 20x + 6 satisfies the three conditions of Rolle's Theorem on [0,5].…

A: