The image presents a multiple-choice question related to complex roots of a polynomial equation. Below is the transcription suitable for an educational website: --- **Question:** Which is a list of all the roots of \( x^3 - x^2 = 4 - 4x \)? **Options:** A. \(-1, 2, -2\) B. \(1, 2, -2\) C. \(-1, 2i, -2i\) D. \(1, 2i, -2i\) --- This question involves algebraic manipulation and the potential use of the quadratic formula or complex numbers to determine the roots of the given polynomial equation. Students are expected to factor the polynomial or apply suitable techniques to find the real and/or complex roots.

Q: Determine the argument and the modulus of the given complex (-2-4i)(5i) number: (3+8i)

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Q: Find the 3 cube roots of -4+4i √3

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Q: (c) Find the 3 distinct roots of 2³-2-2√√3i

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Q: Select one: O a = 1+iv2 and æ = 1 – iv2 O a = -1 - iv/2 and a = -1+i O not in the list O r = -V2 and…

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Q: Find the 4 fourth roots of -8+8i(square root of 3)

A: Let, z=-8+83i Since, nth root of any complex number w is defined as, wn=rncosθ+2kπn+isinθ+2kπn

Q: Which of the following is a root of the polynomial x? – 4x + 13? O A. 3+ 4i O B. 2 – 3i O C. 4- 5i O…

A: We have to find roots

Q: Find the four roots of ( 3 + i4 )

A: We know that , Complex number is of the form , z = x + iy. Also , Polar form of complex number is…

Q: What is the nature of the roots of 2y"+24y+72? O Complex conjugate O None of the above Distinct…

A: Given equation is . Let us denoted it by Now, on compare above equation with We get,

Q: What is the multiplicative inverse of the complex mumber z = 2-5i? 2 В. 29 29 c (1) D. (;=) А. 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: Find the four roots of ( 3+14)

A: The given problem is related with complex analysis. We have to find the four roots of 3 + i4. Note…

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: 4 Get all the roots of 2(V3i – 1) |

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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: Find the two square roots of 4i. A v2+ v2i and v2- V2i B v2-v2i and -V2- V2i © v2- V2i and -v2 - v2i…

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Q: Find one of the roots of 2x3 +3x2 – 23x – 12

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Q: 5. Find a polynomial with real coefficients that has the zeros without complex numbers.) 4,3i, and…

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Q: 3. What are the roots of - 5x2 36 =0 1. (3i, -3i,-2, 2} 2. (-2i, 2i,-3, 3} 3. (9,-4} 4. {-9,9,-4i,…

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Q: Find three (3) distinct roots of the cuberoot of 8 and express the root in rectangular form.

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Q: Find the real component if the

A: Given,             a+bi Here,         a=9,  b=10, and n=7.

Q: What is the 4th roots of z=1+i

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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: Find the roots of (-i +1) all to the power 1/3

A: Our objective is to find the roots of (-i +1) all to the power 1/3

Q: Determine the three roots of -64 . O 2+ j2v3, -4, -2 – j2v2 О2+ 2/3, -4, —2— )2/3 O -4, 2– j2/3, 2+…

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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: Simplify -3j 1234567+ 4j98765432 – 5j-32198765 + 6. What is the imaginary part of the result? O 2

A: Given: -3j1234567+4j98765432-5j-32198765+6

Q: 10. Which of the following are roots of x3- 3x²– 45x-81? -3 and 9 -4 and 8 -2 and -1 -1 and 9

A: Simplification