set C of ordered pairs of real numbers, addition and multiplication are defined by the formulae (a, b)+(c, d)=(a + c, b +d)   and  (a, b).(c, d)=(ac - bd , ad + bc). Show that the system (C,+, .) is a field. What are the additive and multiplicative identities of  of this field

Q: 4. Perform the following operations: a) (4x²+5x+3)+(3x²–2x+8) b) (3r² –7x+2)(5x²+4x-6) c)…

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Q: f(x, y) = logy(3x) af ala ala дх ду ... --- --- --- 000

A: The given function isRewriting the given function,

Q: (22) Let A = (-∞, -2] and B = (102, ∞).

A: Given A=(-∞, -2] , B=(102, ∞). Now, the union of two sets consists all those elements that belong to…

Q: Find the symmetric difference of {1, 3, 5} and {1, 2, 3}.

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Q: Recall that {C, +, ·} is the field of all complex numbers. Introduce a total order < on C as…

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Q: Find, if possible, A + B, A- B, 2A, 2A- B, and B + A = 5-6 2 3 -4 1 (a) A + B 183 11 (b) A - B 188…

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Q: Compute: [2 1 0 5 - ] [ ] -5 ܗ

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Q: Can you please identify the splitting field of (x3 + x2 + 1) over Z3.  Write the addition and…

A: Given,Polynomial: (x3+x2+1)We need to identify the splitting field of x3+x2+1 over Z3.To draw the…

Q: Explain why the ring of integers Z under usual addition and multiplication is not a field.

A: Given that the set of integers Z is a ring under addition and multiplication. We know that an…

Q: 1 -1 A = -1 2 -1 0 -1 1

A: Answer is in next step

Q: Let a = -27 +53 + 4k. Find a.

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Q: verify that 3(A + B) = 3A + 3B

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Q: Is the multiplicative inverse of an element in a polynomial ring unique?  Or can there be more than…

A: This can be proved as shown below:

Q: Let A - 3 -5 4 5 2 B = -1 4 " 1 0 0 Determine the product AB.

A: Given:A=[34​−55​2−5​]B=⎣⎢⎡​−1−11​−440​200​⎦⎥⎤​ The product AB is calculated as…