Let 4 a) Given that In (y) can be written in the form In (v) = In (A) =³ + In (B) =² + In (C) z+ In (D) . What are the coefficients A, B,C, and D ? A =

Q: Show that (n+1)Pn+1(x) = (2n + 1)xp,(x) – npr-1(x) ;n> 1? %3D

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Q: 1. Explain why Corollary 1 of Theorem 9-7 is true. That is, explain why L1 = L2.

A: Given that ∠1=∠2 is true statementsHint: Major arc; Minor arcand…

Q: 10 2. Use De Moivre's theorem to determine 1 in the form a + ib. 2

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Q: X sec10 can 1. Let u = 7 In х2 - 1

A: Given: ∫x sec107ln2x2 - 13tan7ln2x2 - 13dxx2 - 1.

Q: 2. Find all number z such that Az" + Bz² + Cz = D a. A= 2

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: a+ib a) If x+ iy = prove that x? + y² = 1. a-ib

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Q: 2.If alb and alc then al Cbx tcy) for all X>YEZ.

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Q: 1. • If r + 1| < o, prove that |r³ + 1| < 0.331.

A: Here we use the fact  | x |&lt; a implies  -a&lt; x &lt; a .

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Q: 1S prove that (a + b) = a² + b².

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Q: 2. Prove that if 5BA+ AC A - I = A, then A must be inver

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Q: Q4: 1- Prove that (1-0+(1+ () 0. 2. Put in the form a+ib ((1+i))- ((1-i)).

A: Here we have to prove that, 1) 1-i2+(1+i)2=0 2) Put in the form of a+ib, 1+i22-1-i22

Q: α Let V₁ = {(₁)|a € R}. V₁ with standard V4 operations will fail both axiom "close under addition"…

A: Let A be a set and ∘ binary operation on A then 1. We say A is closed under the binary operation ∘…

Q: Express In (2) in the form a + ib. (Simplify your answer completely.) In(z) = BRITK In( 4√2 ) + 1 (…

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Q: Use z = a + bị to show that z + 7 = 2a and z - 7 = 2bi.

A: Given: z=a+ib

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A: We prove that

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Q: According to boolean algebra x.(1 + y) =?

A: We will use the following 3 rules : (i) Distributive law : a•(b+c) = a•b + a•c  (ii) Identity law :…

Q: 3. Prove that Re(2-+z')<4 when z<1.

A: a.          x+y ≤x + y                                             (triangle inequality)b. Re(z1+z2)…

Q: two positive iontages and bare by 2, them prove that. (2° +1) is most divisible by (2²-1) let a with

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Q: _. . Prove that z² = + Emo(-1)" (n + 1) (²2)", where |z-21 < 2.

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Q: It is possible to regress x1 on y. a. True b. Falas

A: From the given dataset we have to check that , is it possible to regress X1 on Y1  or not.

Q: Q) prove that (1) -2P xSinx 2.

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Assume that (8) ∞∑n=1nanxn−1=∞∑n=0anxn∑n=1∞nanxn−1=∑n=0∞anxn for all x, and determine what this…

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Q: Question is attached, Thankyou

A: Let us take z = x + iy.

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A: Complex number which satisfy |z|-z= 2+i

Q: 2 (x) 2. prove that s

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Q: In yz can be written as : 1 In x - In y + In z a O 4 1. In x- In y- Inz b O 4

A: I have Provided this answer in step-2.

Q: If z = 3 – 3i, express 5/z  in the form a + bi

A: The given value of z is z=3-3i.

Q: how that ℝ3 = span( 1 1 2 1 2 1 0 3 -1

A: We want to show that  any vector can be written as linear combination of the three  given vectors…

Q: Show that If |z| = 1, then: -1 = Z

A: z is a complex number. z=a+ib |z|=(a+ib)(a-ib)     =a2-b2 if |z|=1, then a2+b2=1

Q: (ii) A = 82 + &V1+ 4

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Q: D. Let Find 2,-

A: We will find out the required value.

Q: . Let, a, = 1, az = 2, b; = 0, b2 = 1, for n2 3, a, = 2an-1 + bn-1 for n22 b, = br-1+ an-1 express…

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Q: Prove that JI = J [1 0 0] I = |0 1 0 Lo 0 -1 2 -31 J = 4 5 -6 %3D –7 8 -9 1.

A: Considering the matrix multiplication of J and I

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Q: Prove that le-2z| 0.

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Q: Express 3x, xπ, and xsin x using the base e.

A: Our Aim is to express the following function using the base e given below:-(i) 3x(ii) xπ(iii) xsin x

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A: If z =x+ iy then  z = x- iy. i2 =-1.

Q: By expanding both sides of the identity (1+ x)"+4 = (1+x)"(1+x)* prove that ("**) - (") + «(,",) +…

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Q: #02:-Discuss all the cases of reducible to hamggenou D.E form.

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Q: 4. Verify thatf (x) = x³ – x2 – 20x + 6 satisfies the three conditions of Rolle's Theorem on [0,5].…

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Q: Prove the following:  if x^2 = y^2, then x = y or x = -y.

A: Subtract y^2 from both sides.

Q: (a) State the Eisenstein Criterion (without proof). [ (b) Prove that 30x³ 91 does not have roots in…

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