Find all (real) values of b and e such that a³ + bx²y + cxy² + 4y³ +6x +3 с is harmonic on all of C.

Q: -2+3i . Find the complex conjugate, Z. Write your answer in a + ib 3-2 Given Z= form.

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Q: 3. Find the roots of ( x2-1) ( x2 + 3x – 2)=0

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Q: If the roots of the equation x - 8x + a² - 6a = distinct, then find all possible values of a.

A: Since the roots of the given equation are real and distinct, We must have…

Q: What does Descartes’ Rule of Signs tell you about the real roots of x3 – x2 + 1 = 0 ?

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Q: a) State all the alberic properties used in solving for x, 3x-4-3x=2x-x

A: Given:equation To find:write the algebraic properties used to solve for x.As per our guidelines we…

Q: Let p(z) be a polynomial with complex coefficiants and defree less than or equal to 2. It is true…

A: Given that, pz is a polynomial with complex coefficients and the degree less than or equal to 2. A.…

Q: w is an imaginary root of unity. Prove that (i) (a+ba+ca²)³ + (a+ba² +ca)³ = (2a-b-c) (2b-a-c)…

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Q: Let (zn)n≥1 be a geometric progression of complex numbers, and suppose that z3 = −1 and z5 = 7. Find…

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Q: Assume Z₁ = 2 - i and Z₂ = 1 + 3i. Find the product and quotient of z1 and 22. Z₁Z2 = Z1/Z2 =

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Q: 2 Express ( √5 - √5₂) in 2 simplest a + bi form.

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Q: Express all answers in Rectangular Form. 1. (1 + j3)z² + (5 + j6)z + 7 – j6 = 0 2. 3z? – (5 – j4) z…

A: Since you post more than three subparts questions as per our guideline we can solve only first three…

Q: (2) Complex roots: (a) Check that z is a product of linear factors over C. (b) Check that all four…

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Q: a. Factor the polynomial over the set of real numbers. b. Factor the polynomial over the set of…

A: 107. Given polynomial is: fx=x4+2x3+x2+8x-12 We have to factor the above polynomial over the set of…

Q: If a is a non-real complex nth root of unity, find the values of:

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Q: Which of the following expressions has the greatest common monomial factor of 4x y? O 17x3y + 8y3-…

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Q: What is the conjugate of 3- 2/5?

A: conjugate is where we change the sign in the middle of two terms . So ,conjugate is 3+2√5

Q: Gg.73. rind the complex conjugate of t -1 Write your answer in the form

A: Given: t-1 We have to find the complex conjugate of t-1.And write the answer in the form of a+ib.

Q: . Factorize the expression (5 - i)z2 - (3 - 2i)z + e2pie(i)

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Q: Find ||v||. v= - 4i + 7j - 2k v = (Type an exact answer, using radicals as needed.)

A: topic - magnitude of vectors

Q: Verify that z 2 + 4i is a solution of z2 + 6z - 40i = 0. Is 2+ 41 also a solution?

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Q: Prove that zª +1 = (r² + √2x+1)(x² − √√2+1). Then factor z¹+1 into linear factors over the complex…

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Q: Z= 2 + 5j Y= -3 - 3j D= -2 + 6j Find the conjugate of the numbers above

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Q: b. Find the roots of √√√64 e¹.4i

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