7. Find all distinct principal ideals of Z14

Q: Find the characteristic of Z4 ⨁ 4Z.

A: Given: ℤ4⊕4ℤTo find: The characteristic of ℤ4⊕4ℤ.

Q: A = 6. -3 -3 -4 3.

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Q: Write down monic polynomials in R[X] of least possible degree which have the following complex…

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Q: Suppose that x and y are real numbers such that y is 6 greater than x. What is the smallest possible…

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Q: If zz - -4 + j5, z2 - 3 - j2 , and z3 2- j3, what is Im (z - z1) + z; ? Note: 2* is the complex…

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Q: One of the following is an ideal of z1: (0,3} (0,2,4,6} None (9,3,6,9}

A: From given statement

Q: If T: R"„8* is a Linear transfor matiom and m (x)= (2² +2)Cx+ 3. Find all the ratinal canomical ferm…

A: Companion matrix:  Let f(x)=xn+an-1xn-1+………+a0 be a polynomial then the matrix form is given by…

Q: The conjugate of -4 -3i is............

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Q: Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

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Q: Find gcd (272, 1479) and find the integers x, y such that gcd(272, 1479) = 272x + 1479y

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Q: Find the SUM of all the complex zeros of f(x)= x3 + 3x2 + 7x + 10 a.) -1  b.) -2  c.) -3  d.) 0  e.)…

A: It is given that

Q: THE RADICAL OF AN IDEAL IS ALSO AN IDEAL.

A: We have to show that  RADICAL OF AN IDEAL IS AN IDEAL

Q: ıs it true or false  every nonzero ideal in complex space contains a polynomial of degree 1

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Q: Explain why 3Z is not an ideal in Q

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Q: Find all values of z such that z5 =1 - i.

A: Given: z5=1-i, To find: All values of z.

Q: For z=1+i find the product of z and its complex conjugate zZ

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Q: polynomial in V2+i and compute the conjugates of i over Express i as a Q(/2 + i).

A: As per the question we have to express i as a polynomial in (√2 + i) and then compute its conjugate…

Q: Find the harmonic conjugate of the following. 10. х-у2+у

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Q: Show that the nth roots of unity are isomorphic to Zn.

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Q: [12 23 -6 A = 11 –8 13 [7 21 15 The cofactors of the first-row entries are The cofactors of the…

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Q: The k-component of +t is

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