show that when |z3| # |z4l, Izı|+ Iz2| I|z3| – Iz4|| Re(z1 + z2) Iz3 + z4| VI

Q: Determine x and y such that 4 -1 -2 x - Y -4 -3 8 -5 -5 4 1 6 2x + y 1

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Q: 6. Let [√16-X² Find y(2√3) 16-x? 2 16

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Q: 7 Evaluate using Convolution theorem: L-¹{²(²+4)} 2

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Q: 3 1 T(V) = 9- -1 U = 2 V =| 4 T(U) = -3 -3 -2

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Q: тах 2х, + 3x, - хз s.t X1 + 2x2 + x3 = 5 (1) -x1 + x2 + x3 21 (2) X1 + x2 + 2x3 <8 (3) X1 20 (4) X2…

A: Problem is Max Z =  2 x1 + 3 x2 -  x3subject to2 x2 +  x3 = 5-  x1 +  x2 +  x3 ≥ 1x2 + 2 x3 ≤ 8and…

Q: Uzn – V2n = (40 – vo)J2n+1 – (u–1 – v_1)2n+2+b(u_2– v-2) J2n for n>-1. From (2.35) uzn + v2n = (40+…

A: Required equations for calculation: Equation (2.37) u2n-v2n=u0-v0J'2n+1-u-1-v-1J'2n+2+bu-2-v-2J'2n…

Q: Show that Y1 = X1/X2 and Y2 = X1 + X2 are independent and that Y2 isχ2(r1 + r2).

A: Given Y1=X1X2Y2=X1+X2

Q: 2х + 2у + 6z %3 16 2х — у + 42 - 28 -5х - Зу-z %- -10 %3D

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Q: b 2x 1! + 5x 2! + .+ (nt + 1)п! %3D п(п + 1)! + 10 x 3! + .. 2 3 + .. 1 n 1 + + + = 1 - 2! 3! 4! (п…

A: (b) Case 1 : n=1 2×1!+5×2!+10×3!+...+(12+1)1! = 1(1+1)!2×1! = 1(2)!2 = 2 Therefore, the result is…

Q: (x, y) - (-y, x) 4- (x, y)- (. -x) -8 4. (x, y) - (-x, y)

A: A reflection of a point over the y-axis is shown .

Q: Show that 1 1 1 x2 y? z2 (y² – a²)(z² – a²)(z²? – y²) - - ,4

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Q: O max(x,z) О тах(хә 10xz + 3x + z suисh that 3 > 6х + 3z. О mincә 10xz+ 3x + z such that 3 6х + 3z

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Q: 6. If x = -4 and y = 2, then verify that. 7 (ii) - (x+y)= (-2) + Cy

A: 6 Given that x=−47and y=25. We have to verify that −x+y=−x+−y. First take left hand side -x+y…

Q: (2) juhäi 2 x 2 and D A-B and d,2 1, d31 =-2 then 1. • If A = -3 B 0 4 1. x 1,y% -1 2. x -1,y 1 3.…

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Q: Verify that 2. 1 Hint: Consider x 0, x 0 separately

A: To verify

Q: +prove by indirect method that if X+y>5 then x>2 or

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Q: If z1 = -4 + j5, z2 = -3- j2, and z3 = 2 + j3, %3D %3D %3D

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Q: If z1=1-1,z2=-2+4i. Evaluate |2z2-3z12. pdf.

A:

Q: Expand 1/(z2-3z+2) in the region Mode z greater than 2.

A: Given: 1z2-3z+2, where z&gt;2 Calculation: 1z2-3z+2=1z-1z-2                   =1z-2-1z-1…

Q: Show that if ax2 + bx + c = 0 for all x, then a = b = c =0

A: It is given that, ax2+bx+c=0 for all x,  To prove a = b = c = 0

Q: 8²z 8. If z = x + y Inxy, show that x- 8 z + x² 8²z 8y² 8x8y

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Q: Prove x²(x-y)² =x² -y²

A: Substitute x=y in the given equation Then x2(x-y)2=0 ....... (1) and x2-y2=0 ....... (2)

Q: Мaximize z = 3x1 + 5x2 subject to: 4x] + х, < 25 2х, + 3x, < 15 with х, 2 0, х, 2 0.

A: To Maximise  z= 3x1+5x2subjected to : 4x1+x2 ≤25                         2x1+3x2≤15 with…

Q: Va +3b + Va – 3b If x=- Va+36 – Va– 3b prove that 3bx² – 2ax +3b = 0 | - -

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Q: Find positive integers that satisfy x + y + z = 6 x + 5y + 8z = 35 x = i ! y = i

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Q: We have $6,000 to invest in three types of financial products. If we invest x, dollars (in thousands…

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Q: Let X=(1,0, – 1, - V2). Then, ||X||1= Select one: a. -1-V3 b. C. -/3 o d. 2+V2

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Q: 3. Which statement about k (z)= 3z -7z+2 is true?

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Q: Investigate the based on linearization 3 x = x₁ - x₁²³²+x₂z xr 394 - 292 6 Ac

A: This is a question of equilibrium and stability.

Q: y3-3ax2+x3=0,then

A: Given:  y^3 - 3ax^2 + x^3 = 0

Q: evaluate x2 -(xy-y) for x satisfying x/9 -7 = x/2 and satisfying -3y -5=4y+23

A: See the details solution in below

Q: 2. If z = x+iy = (x, y) then (2,-3)(-2, 1) is A. (1,8) C. (-1,-8)

A: Given,             z = x + iy = (x,y) To find   (2,-3)(-2,1)

Q: 2-If x(z) = 2z + 5z¬1 + 6z-3 – z* find x(n). %3D

A: Consider the given equation:   xz=2z+5z-1+6z-3-z4

Q: If ƒ(2)=z²+1 then u(x,y) = 3+y² 3- y² + 1 83+y²-1 3- y²

A: Given  f(z) = z2+1 We know that z = x+iy Hence f = (x+iy)2+1 = x2+2ixy+i2y2+1= x2+2ixy-y2+1

Q: 6. Show that 2x-3- 2x - 5x-3 (a) , x e R, x ± 1. -1

A: Simplification

Q: 3. 2х, X2 = 2 4. 4x, + х х, — Зх, + х; 3 —2 -x, + x2 - 3xz x – 7x 3x1

A: Q3 asked and answered.

Q: If z1 = -4 + j5, z2 = -3 - j2, and z3 = 2 - j3 , what is the simplified form of z – z + 2 ? %3D

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Q: Show that |Aut(Z2 × Z2)| = 6

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Q: Express (i)(T) J3(x) in terms of J₁(x) and Jo(x) (ii) J₂(x) in terms of J₁(x) and Jo(x) (iii) J4…

A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…

Q: x2 = 2 In(x +2) %3D

A: The false position method (also known as Regula-Falsi method) uses the formula:…

Q: 1. Find z for x = 4.7 %3D 2. Find x if z = 3.2

A: Given  Sample is normally distributed with mean 5 and standard deviation 3.8

Q: 1-2х 1 2х+1 а.) 2х-3 х = 1 - х-1 b.) /2х — 2-Vx +6+1-0

A:

Q: If (x1 , y1) = (-3, 1) and (x2 , y2) = (-2, 4), find (y2 - y1) / (x2 - x1)

A: Given, x1, y1=-3, 1x2, y2=-2, 4

Q: 2.2 Use algebraic manipulation to prove that (x +y) · (x + y) = x.

A: As 2 Questions are given, I will solve only the first, We need to Prove that: x+y(x+y¯)=x Solving…

Q: Prove that y = e-3* (Acos 5x - Bsin 5x) + Cx; A, B and C are arbitrary constants will equalto y"(17x…

A: Given,            y =e-3xAcos 5x -Bsin 5x + Cx

Q: What is the zero-product principle?

A: Zero product principle states that if ab=0  then a=0 or b=0 We apply zero product principle while…

Q: Maximize Z = 2x, + 3.x2; st. 5x, + 7x, <35, 4x, +9x, < 36, X1,X2 2 0 and are intergers

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Q: Use generating functions to determine the number of integer solutions for x + y + 2z = 29, x2-2, y >…

A: Given that x+y+2z=29 As for each x,y,z are non negative. The variable for x is, The variable for y…

Q: Ans.w = 5.7971,x = -0.5145, y = 1.1304, and z = 3.4710 2w + 3x – 4y + z = 9 w - 3x + y - z = 5 -2w –…

A: Let's find.