Let z = x + yi, z2 = 1– 0.5i , and z, + z2 = 3 – 1.5i. Find In(z,) – In(z2) %3D A) In(25) ± 2niN D) In(5) + 2nin B) In(8) + 2nin E) In(3) + 2nin C) In(50) ± 2nin F) In(2) + 2nin G) In (;) + 2nin H) In(4) + 2nin A

Q: (a) cos(iz) = cos(iz) (b) sin(iz) = sin (iz) for all z; if and only if z = nлi (n = 0, +1, +2, ...).

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Q: Let u = PQ and v = PR. P = (2, -1, 3), Q = (0, 2, 1), R = (6, 2, –1) %3D (a) Find the component…

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Q: (a) Find all equilibria of N,, 1 = 1.4N,, t= 0, 1, 2,.. (b) Use cobwebbing to determine the…

A: Given: Nt+1=1.4 Nt ;  t=0,1,2,...

Q: 3) y' dx-(xy+y*) dy-o Let the substitution v= i y vx; dy-vdx+xdv %3D )x*dy+(2xyy*) ax -o Let the…

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Q: .15 (ahäi 3) sin(2t + ) 00 %3D e2t-3 e-3 7 e3 4

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Q: 04.2 If x=7i-j+k, y = 3í - j - 5k and z = 9i + j - 3k Show that xx (y+z) = (x x y) + (x x z)

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Q: dw Let w = cos(6x – 6y), where × = r* and y = 3. Find A o dw = 18sin(6r* – 18)r³ dt O dy =…

A: Answer is Option b is correct Explanationo the solution is given below...

Q: 1. Let X1,. , Xn be iid N(0,0), and Y = E X}/n. ... (a) Find EY. (b) Find Var(Y).

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Q: If u = x²/(x² + y²), find ou/ox, du/dy.

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: 1. We can generalize our approach to warto for any state function. Consider: f = 3x²³ - 2xy² for X₂…

A: As per the question, we will verify the above for f=3x3-2xy2. We are given that xi=1, yi=2; xf=5,…

Q: Q2) Discus the existence and uniqueness of the following IVPS: y = x + ys y = x tan (i) (ii) y(1) =…

A: We Know that,

Q: Evaluate: IIncx + y) – dy dx 3 a² \In(2a) – –In(a) – + Ei(-a) – In(a) – In 2 +- Ei(-1) А. B. a*…

A: We are asked to evaluate the double integral:…

Q: 35 x*-30 x*+3 If the Legendre polynomials P,(x) = then: 8 Find 1) S, x P,(x) dx 2) P's(-1) A) Lx*…

A: We will solve both these questions using basic knowledge of Legendre Polynomials.

Q: - dæ. (x² – 5)1/7 Compute

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Q: 3. Find dz/Ou and dz/du. (a) z = 9x*y- r+ 5y; X = UV; Y =v – u (b) z = 2e*". 1 a= vuv: y=

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Q: [2 1] Q2) Assume A = |1 3 L3 4] - anda-: [2 4 1 B = show that (AB)' = B' A' 13 6 4

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Q: Show the following results used in the class: S =(z1 - E1)² = (zn - n)In = %3D %3D S (-)3D %3D iml…

A: Given that Sxx = ∑xi-x12       = ∑i=1nxi12 + x12 - 2xi1·x1= ∑i=1nxi12 + nx12 - 2xi1·x1 ∑i=1nxi12=…

Q: be a vector space

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Q: is harmo Q4) Find the result of the following: Find z for Inz = 1-in? 1. 2. I (7/2) =? (Gamma…

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Q: [2 1] and B = 1 3 4] 13 2 4 Q2) Assume A = show that (AB)' = B' A' 3 6

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Q: [2 1] Q2) Assume A = 1 3 [3 4 T2 4 and B = show that (AB)' = B' A' %3D %3D [3 6

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Q: 4. Given that z₁ = 1-5i and 22 = 3 + 4i, find (a) Z1/Z2 (b) Z1/Z2 (c) 21/Z2

A: As per our guidelines we can answer only 3 subparts of the given question so kindly repost the…

Q: 2x-1 3 + If y = Vx2 - x then y' = 3 3 x2-x FO

A: We have given y. We have to identify y' is true or not.

Q: 3. Find a closed form for sn = i-1 (15 — 5і). Sn (3 – 8i). 4. Find a closed form for sn = i=1 Sn ||…

A: close form is given below

Q: SSR is defined by SSR = E9 - 9). Prove %3D (1) SSR = 3} S.z- (2) E(SSR) = o + Bị Sr. (3) Show MSR ~…

A: Given, SSR=∑i=1ny^i-y¯2. The fitted equation of yi=β0+β1xi+εi is  y^i=β^0+β^1xi, for i=1,2,...,n. yi…

Q: п(п- 1) (п + 1) n Prove that i² – i = | 3 i=0

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Q: W.Find A' for the given cholce of U. 1A (3,6, 9) U (x/0<x$ 10 A 2. A = (1, 2, 3) U = (0, 1, 2, 3, 4,…

A: From the given information we find the A compliment .

Q: 15. r(() — а + tb +f'e

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Q: y" +3y + 2y = denkleminin özel çözümü y; aşağıdakilerden hangisidir? %3D +1 O a. y5 = ze2 - e In(1+…

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Q: Suppose that at ~ WN (0, 1). (a) calculate the ACF of xt = at +0.5at-5; (b) calculate the ACF and…

A: Given We are required to solve part (a) to (d).

Q: Let = r, (cos 0, + isin 0, ) and r, (cos 0, + i sin 0, ). Z, = X1 + iy, 1 Z 2 X2 + iy, Then show…

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Q: Given v(z) = Vcos(In(z)) which of the following represents v'(z)?

A: Given: v(z)=cos(lnz)