3. Show that (1+i) = 2i

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Q: Let X and Y be independent, and let X be N(10, 1) and Y be N(11, 1). PIX >Y),

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A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: verify the given equation. 16.∞∑n=0an(x−1)n+1=∞∑n=1an−1(x−1)n

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Q: Consider a, = V4n² + 3n – 2n for n > 1. %3D -

A: Introduction: The sequence is a set of functions with the set of natural numbers as the domain of…

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Q: Compute: 2i J25 -4i A a Answer: 1,

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Q: Solve the Auxiliary DE 75. и"" + u" — 2и 3D 0

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Q: 22. Differentiate the following with respect to the variable x, giving your answer in a implified…

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A: We have to express 4x + 4x as a single power of 4.

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Q: Prove that Σ", (2i-1)-. .

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Q: у" + Зу" + Зу' +у%3D0

A: We have to solve the differential equations

Q: 4. Prove that 3i² + i = n(n+ 1)?

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Q: Given that 32a × 11º = 274x × 332× express a in terms of x?

A: Find your answer below

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Q: 4. If ā= 3i - 2j and b=-5i- j, express 3 a -b in terms of i and j.

A: This is a vector problem

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Q: Perform the indicated calculations. 2(2 + 1 + 2) in Z3

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Q: 2) × if it was 2+4i and 2=3-1 3+1 2+i 2 prove that x² + 3xy + y² = 6 =

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Q: Compute: (i-2) (i+2) Answer: 2.

A: Solution: The objective is to compute the given equation

Q: 1. Show that (a) exp(2±3лi) = -e²; (c) exp(z+лi) = - expz. πί p ( ² + 7² ) = √ = (1 + i); 4 (b) exp

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Q: What's the value of the integral (2 - 1) dz from (1+i) to (2+2i) a. 17 + 11i b. (11 + 10i) /3 C.…

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Q: у" — бу" + 11у' — бу — 4sin7х + 5 - %3D -

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Q: 2 Xi. にく prove thate 2.

A: Given that  We have to prove the given expression:

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Q: 2ху 3. y' = -x?

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Q: 5. Solve: 4xy2(3x³y – 5xy) = 0, Let y = 2 %3D

A: A detailed solution is given below

Q: 1. • convert to Looarithmie form = SX 3. 3 %3D 34-1 4. = 2x = Sxtl

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Q: 5] compute: 7A -5B where: 2+3i itqi -si A = 3+7i -4 ?b-8 7 3ti 2+si ?5-8 5-2i -4-3i 8ミ チ+

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Q: 3 1 If A = show that A²- 5A + 7I = 0. %3D -1 2

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Q: 3 If A = 1] show that A² - 5A + 7I = 0. %3D %3D -1 2

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Q: В Calculate A and B so that + %D 1+x 1-

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Q: & B= Q1-Let A = 2 4 Verify that (AB)" = B" A"

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Q: AB = 8 %3D M2PQR = 140° %3D O y= 1 x is seven units greater than y. MLABC = 122° %3D PQ = 3 MAY tv…

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Q: Compute for the value of tanh-(1 – i) In 5 my + 2.13i In /2 + 2.13i Inv - 4.25i 2 In /2 + 2.13i

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Q: dt 7) /2-t

A: 7).∫-∞-2dt/2-t                         = ∫-∞-2(2-t)-1/2dt