Let u be an nth root of unity. Show that u-1 is also an nth root of unity.

Q: An nth degree polynomial will have at most n+1 real roots. O True O False

A: No, that is not possible. The only reason that an n-degree polynomial has max n roots is that it can…

Q: Let = e²i/n be an n-th root of unity. Show that (k(1-n) Resck (27²1) n for all 0 <k<n-1. =

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Q: Determine the zero(s), if they exist.

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

Q: QV2 | is Principal Ideal Domain.. True False

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

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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: 5. Use the Intermediate Value Theorem (IVT) to show that the equation below has a root in the…

A: Given that, The function is, f(x) = 2x3 + x2 + x + 3 = 0 interval is = (-2, 0) We have to prove by…

Q: Let a EC be a primitive nth root of unity.

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Q: Exercise 9. We can find a non-constant polynomial that is bounded over the set of complex numbers.…

A: This is false

Q: For any n &gt;1, prove that the sum of all the nth roots of unity is 0.

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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: If a, B are the roots of the equation x + px + q =0 and also of x + p"x" + q* = 0 %3! αβ and If are…

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Q: Find all the numbers z such that e^2iz= 5i.

A: We are given : e2iz=5i Now Using  Euler's equation: ( eix=cos x+i sinx) ⇒e2iz=cos (2z) +i sin(2z)…

Q: Show that each of the following numbers is algebraic over Q by finding the minimal polynomial of the…

A: Algebraic Number- Let E and F be fields and E is an extension of F. A number 'a' in E is called…

Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

Q: a) Solve for x in the following questior 7-x = 1 %3D

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Q: (10') Use Rouche's theorem to find the number of roots of 2z4 – 5z + 1 = 0 (1) for |z| < 1 (2) for…

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Q: For any n &gt; 1, prove that the product of the nth roots of unity is(-1)n+1.

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Q: The set of exhaustive values of m for which both roots of the equation x2 – 2mx + m2 – 1 = 0 are…

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Q: QV2 is Principal Ideal Domain. True False

A: A principal ideal domain is an integral domain in which every proper ideal can be generated by a…

Q: 1. Show that the function p() = x + 4x3 – 9 has two real roots, that is, there exist r1, r2 ER such…

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Q: Find all other zeros of P(r) =x - x + 2, given that 1 + i is a zer 2 If there is more than one zero,…

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Q: a) Calculate the 4th roots of (5-j3)

A: The objective is to calculate the 4th roots of (5-j 3).

Q: Find p so that  x2 - 6x + p = 0  has one root (i.e. is a perfect square)

A: We will solve it by two methods Shortcut method to find p for the equation given is x2 + b x + c  is…

Q: 8. Find all the roots of f(x) = x' - 4x' +6x² – 4x+5 if 2– i is one root.

A: We will find all the remaining roots as following.

Q: a) Compute the absolute value and the conjugate of z= (1+i)°

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Q: 13 is a root of 3x? - kx - (k + 73) = 0. 3 1. Find k such that-

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Q: QV2] is Principal Ideal Domain. True False

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Q: Prove that the roots of ax+4=2x²-bx are real for all values of a and b

A: The nature of roots of a quadratic equation Ax2+Bx+C=0  is:

Q: Use Cramer's rule to find only the value of x2 , where a is a positive real number. 2x2 – x3 + x4 =…

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Q: (b) Let A₁, A2, · · ·, №46 be the roots of 2¹ 1/46 that 46 Σλ = 0 i=1 . Show

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Q: Use the Newton-Raphson method to determine the real root of: f (x) = -1 + 5.5x - 4x + 0.5x using x,…

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Q: Let K be a finite extension of Q. Show that K contains only finitely many roots of unity.

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Q: Q:If a.ß are roots of ax +2bx +c = 0 and a + 8.ß + 8 be those of b2 - ac в— АС a Ax +2Bx + C = 0,…

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Q: Let a be a positive real number and I = , Sdydx. 1 2vx

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Q: Let [a] be a non-zero element of Z43. w| 42. When is an element of Z43 said to be a primitive root?

A: This question is based on primitive roots. We recall the definition and give couple of examples.

Q: #8a using Descartes's rule of sign

A: Prove in the following that if all the coefficients of an equation are positive and the equation…

Q: Find all roots of x^4-7x^3+18x^2-22x+12 fiven that 1-i is a zero and sketch the graph

A: We have to find all roots of x4-7x3+18x2-22x+12. Given that 1-i is a zero.   We know, if (x-a) is a…

Q: A quadratic fuction f is given in photo provide

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Q: a) Compute the four 4th roots of −T + Ti

A: Compute the fourth roots of z=-T+Ti, where T is any arbitrary real number.

Q: Explain the relationship between ideal and subring

A: A subring S of a ring R is a subset of R which is a ring under the same operations as R.   An ideal…

Q: (b) For all positive integers n, show that the value of un is the sum of the primitive nth roots of…

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Q: Prove that the product of all the distinct nth roots of 1 is ( - l)n+ 1

A: Let us complex number zz=(1)1n apply power n on both sidezn=1zn-1=0

Q: Use Bisection method to find a real root of x2 -2 in the interval [1,2]. What should be xg Xn Xn…

A: As  f(x)=x2-2, in [1,2]Therefore,  f(xn-)=f(1.40625)                            =(1.40625)2-2…

Q: show that the polynomial p(x) = x^3 - 8x + 6 has exactly two roots on [0,3]

A: The given polynomial is p(x)=x3-8x+6. The roots of this polynomial are the values of x, where its…

Q: Find a polynomlal f (x) of degree 3 that has the following zeros. 5, -7, 6 Leave your answer in…

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Q: Determine one real root of 2xcos2x – (I on the interval (2, 3)using the Regula-Falsi

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Q: Let h(x) = x3. Use the Intermediate Value Theorem to show that there is a number between 2 and 3…

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Q: use the intermediate value theorem to show that there is a root of x^4+x-8=0 in the interval (1,2)

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Q: Find the number in {x E R:-2<x<2} such that the sum of that number and its square is a maximum.…

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