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Which of the following statements are true ?
(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes.
(2) For any polynomial f(x) =0 with real co-efficients, imaginary roots occurs in conjugate paris.
(3) Order relation exists in complex numbers whereas it does not exist in real numbers.
(4) The value of ω used as a cube root of unity and as a fourth root of unity are different.
(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes.
(2) For any polynomial f(x) =0 with real co-efficients, imaginary roots occurs in conjugate paris.
(3) Order relation exists in complex numbers whereas it does not exist in real numbers.
(4) The value of ω used as a cube root of unity and as a fourth root of unity are different.
- a)(1) and (2) only
- b)(2) and (4) only
- c)(3) and (4) only
- d)(1),(2) and (4) only
Correct answer is option 'B'. Can you explain this answer?
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Which of the following statements are true ?(1) The amplitude of the p...
Imaginary roots always occur in pairs. w is just a variable. it can take any value according to the nth root taken
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Which of the following statements are true ?(1) The amplitude of the p...
(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes. This statement is true. The amplitude of a complex number is the magnitude or absolute value of the number, and when you take the product of two complex numbers, the absolute values of the numbers multiply together.
(2) For any polynomial f(x) =0 with real coefficients, imaginary roots occur in conjugate pairs. This statement is true. This is known as the conjugate root theorem, which states that if a polynomial with real coefficients has an imaginary root, then its conjugate (with the sign of the imaginary part flipped) is also a root.
(3) Order relation exists in complex numbers whereas it does not exist in real numbers. This statement is false. The real numbers have a natural order relation, where one number can be greater than, less than, or equal to another number. However, complex numbers do not have a natural order relation. It is not meaningful to say that one complex number is greater than or less than another.
(4) The value of e^(πi) is equal to -1. This statement is true. This is known as Euler's identity, which states that e^(πi) + 1 = 0.
(2) For any polynomial f(x) =0 with real coefficients, imaginary roots occur in conjugate pairs. This statement is true. This is known as the conjugate root theorem, which states that if a polynomial with real coefficients has an imaginary root, then its conjugate (with the sign of the imaginary part flipped) is also a root.
(3) Order relation exists in complex numbers whereas it does not exist in real numbers. This statement is false. The real numbers have a natural order relation, where one number can be greater than, less than, or equal to another number. However, complex numbers do not have a natural order relation. It is not meaningful to say that one complex number is greater than or less than another.
(4) The value of e^(πi) is equal to -1. This statement is true. This is known as Euler's identity, which states that e^(πi) + 1 = 0.
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Which of the following statements are true ?(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes.(2) For any polynomial f(x) =0 with real co-efficients, imaginary roots occurs in conjugate paris.(3) Order relation exists in complex numbers whereas it does not exist in real numbers.(4) The value of ω used as a cube root of unity and as a fourth root of unity are different.a)(1) and (2) onlyb)(2) and (4) onlyc)(3) and (4) onlyd)(1),(2) and (4) onlyCorrect answer is option 'B'. Can you explain this answer?
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Which of the following statements are true ?(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes.(2) For any polynomial f(x) =0 with real co-efficients, imaginary roots occurs in conjugate paris.(3) Order relation exists in complex numbers whereas it does not exist in real numbers.(4) The value of ω used as a cube root of unity and as a fourth root of unity are different.a)(1) and (2) onlyb)(2) and (4) onlyc)(3) and (4) onlyd)(1),(2) and (4) onlyCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Which of the following statements are true ?(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes.(2) For any polynomial f(x) =0 with real co-efficients, imaginary roots occurs in conjugate paris.(3) Order relation exists in complex numbers whereas it does not exist in real numbers.(4) The value of ω used as a cube root of unity and as a fourth root of unity are different.a)(1) and (2) onlyb)(2) and (4) onlyc)(3) and (4) onlyd)(1),(2) and (4) onlyCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements are true ?(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes.(2) For any polynomial f(x) =0 with real co-efficients, imaginary roots occurs in conjugate paris.(3) Order relation exists in complex numbers whereas it does not exist in real numbers.(4) The value of ω used as a cube root of unity and as a fourth root of unity are different.a)(1) and (2) onlyb)(2) and (4) onlyc)(3) and (4) onlyd)(1),(2) and (4) onlyCorrect answer is option 'B'. Can you explain this answer?.
Which of the following statements are true ?(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes.(2) For any polynomial f(x) =0 with real co-efficients, imaginary roots occurs in conjugate paris.(3) Order relation exists in complex numbers whereas it does not exist in real numbers.(4) The value of ω used as a cube root of unity and as a fourth root of unity are different.a)(1) and (2) onlyb)(2) and (4) onlyc)(3) and (4) onlyd)(1),(2) and (4) onlyCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Which of the following statements are true ?(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes.(2) For any polynomial f(x) =0 with real co-efficients, imaginary roots occurs in conjugate paris.(3) Order relation exists in complex numbers whereas it does not exist in real numbers.(4) The value of ω used as a cube root of unity and as a fourth root of unity are different.a)(1) and (2) onlyb)(2) and (4) onlyc)(3) and (4) onlyd)(1),(2) and (4) onlyCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements are true ?(1) The amplitude of the product of complex numbers is equal to the product of their amplitudes.(2) For any polynomial f(x) =0 with real co-efficients, imaginary roots occurs in conjugate paris.(3) Order relation exists in complex numbers whereas it does not exist in real numbers.(4) The value of ω used as a cube root of unity and as a fourth root of unity are different.a)(1) and (2) onlyb)(2) and (4) onlyc)(3) and (4) onlyd)(1),(2) and (4) onlyCorrect answer is option 'B'. Can you explain this answer?.
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