Complex Analysis Prove the following

Q: Establish an iterative procedure to determine the root of the polynomial y = f(x) = x³ + 2x – 4

A: Iterative method.

Q: f(x)=sin(x) is of order 1.

A:

Q: Abstract Algebra

A: To find the smallest degree polynomial f(x) with coefficients in Q, such that f(√2+√3)=0.

Q: 4. Evaluate - 2 sin(32) dr.

A:

Q: Evaluate (1 + i)(¹ - i). (1

A:

Q: 3) Evaluate 10log (x-5)

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Q: Prove that if a, b e R, then (a) -(a+b) = (-a) + (-b), (b) (-a)·(-b) = a · b,

A: (a) Proof of the fact -(a+b)=(-a)+(-b): Since -1 is additive inverse of 1, hence  −1+1=0   (zero in…

Q: - 3x₁ + x₂ + 3x3 = -8 3 x₁ + 4x₂ + 2x3 = 13 2x1 +3x2 + 4x3 = 16

A: Here we have to find solution i.e x1 , x2, x3

Q: Lim メー→& 5X 2X+XSin3 X -2X++

A:

Q: Example Evaluate +f -P) dpdgdr (p2 + q² – r²) dp dq dr + pq² – pr2 dq dr 3 1 + q? ² – r? } dqdr 3 -…

A: Let's find.

Q: Linear Algebra show calculations

A: Step 1: Step 2: Step 3: Step 4:

Q: 4 x₁ +5x₂ +3 x3 = -27 2x₁ + 6x₂+2x3 = -15 2x₁ - x₂ + x3 = 12

A: The given system of linear equations, 4x1+5x2+3x3=-272x1+6x2+2x3=-152x1-x2+x3=12 We have to find…

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

A:

Q: (a) Calculate (a +36). C where a = (0, -1, 0, 1), 6 = (1,-1, 1, -1) and c = (2,2,3, -3) (b)…

A:

Q: QUESTION 2: (Interpolating and Polynomials approximation) Use Lagrange's formula and estimate from…

A: Given data is: Income not exceeding (in JD) 295 410 585 730 No. of workers 36 44 51 62 To…

Q: Using linear algebra to find x1,x2,x3

A: Introduction: Row operations are used to convert a matrix to row-reduced echelon form, which is…

Q: 2 + J 3 5- j3 Simplity usingg exponeutical

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Q: 2+i Evaluate (2x+1+iy)dz along (1-i) to (2+i) 1-i

A:

Q: (²)

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Q: 1337 i+1` Compute ()

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Q: 2 -2 a) Evaluate by Chio's method -2 1 1 0 -1 0

A: Solution is given below:

Q: QUESTION 3 Construct the Operation Table for U(15)

A: Cayley table

Q: Show that f(x) = 3x - 4 is bijective.

A:

Q: If µ(x) ef (x) is an integrating factor of linear D. E x y' + xf(x) y = x* y – x² sin x where f' (1)…

A: To find - If μx = efx is an integrating factor of linear D.E. x3y' + xfx y = x4y - x2 sinx, where…

Q: Proof that: 12-a) =r → そ= a+re

A: The solution is:

Q: 2.x – 3iy + 4ix – 2y -5–10ix =x+ y– iy +2– (3 – x)i D. Find real numbers x and y such that

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Q: II 10. Statements Rease 10(1-) = 8 %3D 10(1–) _ 8 10 10 8 10 %3D 1 = ÷+ 7.

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Q: Discrete Math Show that f(x) = 3x - 5 is a bijection

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Q: 14. 2x 8. 2x, 3x + 6x 2x

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Q: ら()-20 (4)-a(4) +20 20-20 16-36+20 らメ-20 x-4)(x-5)

A: Domain: - The domain of a function is the entire range of possible independent variable values.

Q: linear algebra   What does Span {v1,v2,v3} mean how  do I explain this

A: Solution:

Q: 13. Arrange the terms of the following polynomials in descending and ascending powers of y. (a) 8+2y…

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

Q: 1f \ x | < 1 and 1= x < < 1; then: 2 ₂ F₁ (a, b ; c ; x ) = (1 − x)¯ª₂ F₁ [a, c − b; c; X _— — ₁) X-

A:

Q: Property of zero algebraic properties addition

A: To explain: Property of zero in addition