2. (a) Show that 25 – 32 = (z – 2)(16 + 8z + 4z² + 2z³ + z4). (b) Find the roots of 16 + 8z + 4z2 + 2z3 + z4 = 0 by using De Moivre's theorem to solve 25 – 32 = 0.

Q: Determine the all the roots of z4 +1 = 0

A:

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: f 2 is one root of the equation 4x3 + kx – 24 = 0, then the value of k is       8   –1…

A: The standard form of a cubic equation is given by ax3+bx2+cx+d=0, where a≠0. If a=0, the cubic…

Q: If p(q-r) x² + q (r-p)x+r(p-q) = 0 has equal roots, then 2 1 T= 9 prove that Р + 1 r

A:

Q: The quadratic equation a? – 7x – 18 factorizes to: O (x + 2)(x + 9) O (x + 2)(x – 9) О (х - 2) (х +…

A: Factorize the equation

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)…

A:

Q: Example 2.40. Solve x¹-5x³+20x² 40x+60=0, given that all the roots of f(x) = 0 are complex, by using…

A: Here we need to solve equations using Lin-Bairstow Method.

Q: Solve the following quadratic by square rooting. 0 = 3z2 + 18 The solutions are and L. L.

A: Answer

Q: 2) Find Possible Positive, Negative or Imaginary Zeros. f(x) = -2x° + x² - 8x + 3 %3D Count the…

A: Introduction: In algebra, Descartes' rule of signs is a rule for estimating the maximum number of…

Q: Prove that there are no integer solutions to the equation x² = 4y + 3

A: To prove that there are no integer solutions to the equation…

Q: 4 Get all the roots of 2(V3i – 1) |

A:

Q: Determine the solutions of each quadratic equation by extracting the square roots a) (Зх — 3)2 — 363…

A:

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: Find all integer solutions to the diophantine equation 64x + 43y = 1.

A:

Q: (b) Use the three-digit rounding (and the method of rationalization if appropriate) to express the…

A:

Q: 3) Find all the roots of the following equations z = √1-i 14 b) c) Z - i z = z = 964

A: a)

Q: 2. Explain how you would use each method to solve the equa- tion x? – 4x – 5 = 0. (a) By factoring:…

A: The solution of the quadratic equation of the form ax2+bx+c=0 can be calculated by using integer…

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

A:

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

A:

Q: 2 The roots of the equation X + 2x+ 5 0 a 1) -3 and 1 2) -1, only 3)-1+ 2i and 1- 2i 4) -1+4i and…

A: given equation :

Q: Name Instructor: Stephanie Tran Date Precalculus Preparatory Material This worksheet is material…

A: Given:

Q: Factorize the expressions completely. 1) 4x2 – 36 2) 2x²y – 10xy² – 18xyz 3) х* + 2х — 8

A: Question 1:Given,            4x2 - 36

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

A:

Q: 3. Find the four roots of z=21-3

A: If  then kth root is  where A complex number  can be written as  where is the modulus and  is the…

Q: Find all solutions for x in [0,2pi) 3cosx+4sinxcosx=0 (How do you factor this. . . lol)

A:

Q: Prove that there are no integer solutions to the equation x2 = 4y + 3

A: Given equation:- x²=4y+3  We have to prove that the given equation don't satisfy integer pair of x…