6. Show that when ) < |z - 1| < 2, e - ( - 3) (2 - 1)(2 – 3) Complex Analysis n=0 (z-1)" 2+2 2(z-1)

Q: Let p(x) = ax² + bx + 2 IF be a polynomial of degree two then p(2) is equal to P(-2) = 18 and p(3) =…

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Q: . If f(x) = - x and g a) (f + g)(x) = \\+2x (4-x)+(3x+7) = 11 + 2x c) (f. g)(x) = (4-x)-(3x+²7)…

A: We are given the functions and we need to find out the following functions as given in the question.

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

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Q: 3. Find the number of zeros 1< |z| < 2. (counting multiplicity) of 2z5 – 6z² + z +1 inside

A: We need to find zeroes of  2z5 - 6z2 + z + 1 inside  1 ≤ z &lt; 2. We know about , Rouche's theorem,…

Q: a) x + x+X b) y+y- d) z +2+2+2z+2+2= w+w+W+w+w- e) k+k= na+a+a+a+a- h)t+t+1+1- expresión: 9)1+f+1 ie…

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Q: S(x + 1)(2 – x)° dx 7(2 - x)* - (2 - x)* +c 7(2 - x)* -(2 – x)* +c 3. (2 - x)* +(2 – x)* +c 금(2-x)*…

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Q: (x – 2)²(x+3) (x - 1) (x+2) 6) Let R(x)

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Q: 6. Show that when 0</z - 11 < 2, Complex Analysis (z-1)" (2-1)(2-3)=-3 (2- #=() 2(z-1)

A: Here we prove this statement by using series expansion.

Q: Ex: 5 R T Ex: 5 R (ED) -¯¯ T (ED Т 4 -2x1x₂x3 x1 + 2x3 Ex: 5 Ex: 5

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Q: Find the equation of the line, if the perpendicular drawn from the origin makes an angle 30° with…

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Q: b. Prove Theorem 3.16: Let a be an element of a group G. The centralizer of a in G is a subgroup of…

A: See the detailed solution below.

Q: (16) Show that: (1) The function f(z) is continuous in all complex plane. (2) (-1+i)-8(1+i).

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Q: Given the complex-valued function 1+z z² Evaluate f (¹) (A) -4-3i (B) - f(z) = (C) −¹+²i (D) none of…

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Q: 6. Show that when 0 < |-1|< 2, (z-1)(z-3) Complex Analysis (z-1)" 2+2 =-36 z−3) ² A=0 2(z-1)

A: We use substitution and Laurent series expansion.

Q: ;0<x<0, - 0 <0 <0 Let X,,X,X,r(x;e)=- e.w Discuss the sufficiency by using Factorization Theorem.

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Q: Show that if s(3) 4(q- _9−2+9(1+ 93 2(g-1) increasing or decreasing. For 3 > 0, q> 3

A: The given function is                               sβ=q-2+q1+4q-1qβ122q-1 where β&gt;0 and q&gt;3.…

Q: Question Is f(x) = a4n-2 „4n–4 + x4n-6 + ...+ x² – 1 divisible by g(x) = xª – 1?

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Q: Find the state-space form of the following mathematical model x₁ +2(x₁ - x3)-2(x₂ − x₂ ) - ² (x₂-x₁)…

A: Given Information:The system of equation is given as:To find:The state-space form of the system as…

Q: hd the invense transformof eack of t FX) 6x-5 FCx)=

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

Q: (a) Prove that 1^2+2^2+3^2+………..+n2= n(n+1) (2n+1) divided by 6 For all positive integers n.  (b)…

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Q: Let h(x) = -3) Then, h(x) has a zero on (0, o). —1) (ӕ+2)(2+3а) O True False

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Q: 6/30° + j5 – 3 (а) -1+j+2ej45° (15 – j7)(3+ j2)* (b) - (4 + j6)*(3/70°) means you need to conjugate…

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Q: 5. (a) Find all singular points of (x³ + x² - 5x³x² + 8x - 4)y" + (5x + 10)y' + (10x − 10)y=0 -…

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Q: Given that f(z) = (z+ 2)(z²z+4) Find f(1 - 2i)

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Q: erfind the first agd decond derivatives oh the funchan

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Q: Z +1 f(z) %3D (z – 1)? (z – 2) what will its residue at z = 1? %3D

A: Introduction :

Q: If f (x) = 1 x-7 then f-1 (x) =2x+7                   2                    2) If f (x) = {(-3,1)…

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Q: 2. Determine whether the polynomial 1+ x + ? is a linear combination of P, = 2+x+x², p, = 1-x, p, =…

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