1-i Simplify 1-i in exponential form. Hence find all roots for s V3 + i 3 +i

Q: 7. 2xyy' + (x2 – 1)y² = x²e*

A:

Q: 1 Given z1 = 2 + i and z2 = 3-4i , find Z1 1 in the form of a + ib. Z2 +

A: Given that z1=2+I and z2=3-4i

Q: use Euler methol t solve 9 =2-29 れeon て )こ 2

A:

Q: 16 Solve the equation using Jacobi's method until 5 iterations. (Non-anonymous question (1) 5x₁ - x₂…

A:

Q: (a) b, = (1) The coefficients (b, ) of the Fourier series of the function f(x)%3 sin x; -7<x<r, is…

A:

Q: 0.2-Expand the following in: f(x) = X-1 0<x<1 a- Fourier series of sines only. b- Fourier series of…

A: 2 Given function is fx=x−1, 0&lt;x&lt;1 a We have to find the Fourier sine series of the given…

Q: (b) Solve the given the function and show that its Fourier series is given by, 1. 2 ¬(-1)**'…

A:

Q: 1) The formula for the deficit in the pension fund of a large company is given by y (in millions of…

A:

Q: 3) 12 Glven a = Solve for Vo-

A: Given a=vf-votWe now solve for vo

Q: Determine the quotient of 4(cos 250 - i sin 250) and 2 (cos 15 - i sin 15) A 2 (cos 235 + i sin 235)…

A: We have to find quotient

Q: 10 3. Prove that the L{10e2} = s-2

A:

Q: 4 Find the roots of Z'+1=0_ Hint s i -e t.

A: We have to find root of z^4+1=0

Q: The real roots of e 3x + bx 3 – cx =0 if b= 1 and c = 27 can be determined using Fixed Point…

A: Given equation is  e3x+x3-27x=0 possible form :- x=27x-e3x3 In general:- xn+1=27xn-e3xn3 initial…

Q: where a, b, c are nonzero real numbers such that 6² – ac = 0. Show that if we let r = and y = t,…

A:

Q: Q5) Find the complex exponential Fourier series representation of the following signal 1 -2 -3 3 -1

A: We will be using standard definition

Q: 9.1. Find all values of z such that (a). e = -2, (b). e² = 1+ v3i, (c). exp(2z – 1) = 1, (d). sin z…

A:

Q: Derivatives of sinn x Calculate the following derivatives using theProduct Rule.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Give values for the Fourier sine series S(x) = ) Bn sin 00 (-) пт %3D 4 n-1 S(4) = S(-1) = S(7) =

A:

Q: Find the principal values of each & express the result in rectangular form: 1. (- j) raise to j 2.…

A: (As per bartleby guidelines, for questions containing multiple subparts, only first three subparts…

Q: 1 11. Degree: 7; Roots: x =, x= 3-i, x = 5' 1 X =-7 3

A: Topic :- Alzebra

Q: 5. Given z = 3 – i, find the i. Modulus ii. Argument Hence, express z in trigonometric and…

A: The modulus and argument of complex number is given as follows :

Q: Let w E C with w³ = -V3 + i. Determine all solutions w of the equation. Be sure to make the…

A: It is given that ω3=i-3 so the modulus is 1+3=2 and the argument is tan-1-13=5π6 So ω3=i-3=2ei5π6

Q: The real roots of e 3x + bx 3 - cx =0 if b = 1 and c = 27 can be determined using Fixed Point…

A:

Q: The real roots of e 3x + bx 3 - cx 0 if b = 1 and c = 27 can be determined using Fixed Point…

A:

Q: The real roots of e 3x + bx 3 – cx=0 if b=1 and c = 27 can be determined using Fixed Point Iteration…

A: Given that,e3x+bx3-cx=0b=1, c=27Substituting the values of b and c, we get,e3x+x3-27x=0Initial guess…

Q: Exercise 1: Find a root of the equation X6-x -1 = 0 (Note that the true root is a = 1.134724138.) We…

A: Numerical methods can be used to estimate the root of an equation. Newton-Raphson method uses the…

Q: Solve a0 = 1, and an = 3an−1, for n ≥ 1 using the characteristic equation method.

A: We will start with the trial solution, an = rn to find the characteristic equation.

Q: 40. It is easy to check that f(r) =r² – 4x has two roots. Find these two roots using %3D Newton's…

A: It is given that

Q: -2) Calculate A-1 by 2 Let A = 1 2 1 -1 -1 A-' = ÷(-A² + 3A +I). and verify your result by showing…

A: Given: A=12-2121-1-10 Therefore,…

Q: Find all solutions to 2cos(θ)= −1 on the interval 0≤θ<2π

A: Topic - trigonometric Equations

Q: 1-x 2 3 If 0 x 0 = 0, then its roots are: O only O 0,1 O 1 only O none of these O

A:

Q: If f(x) = 4x, (-7, 7), then the constant term a,of Fourier series is a) 7 b) 47 c) d) 0

A: We have to find the constant terms for Fourier series which we can find by using the formula for the…

Q: |1–x 2 3| If 0 x 0 = 0, then its roots are: O only O 0,1 O 1 only O none of these O

A:

Q: 4. Evaluate and leave your answer in exponential form r(2+ i)+ iy(2 - i)- = 3(1- 2i)1. Where r, y ER

A: Givenx2+i-1+iy2-i-1=3(1-2i)-1  where x,y∈ℝTo evaluate and leve answer in exponential…

Q: d2n-1 2-1 (xsin x) = (-1)"-1¹(xcosx + (2n-1) sinx). To solve this problem use mathematical…

A: The objective of the question is providing the given identity.

Q: Let b₁ 2 = sin−¹ (²) and c, = sin-¹ („²7) for all n € N such that n ≥ 2 +00 Σ(1+bn) n=2 Σ(bn-Cn) n=2…

A:

Q: Find o v' (+2) dt. Show the computations that lead to your answer

A:

Q: 5. Find the roots/s using Secant Method a) x*-x - 10 = 0 b) x- sin(x) –= 0 Ans. x = -1.697 and 1.855…

A:

Q: (a) Find Maclaurin expansions for sin 2x, cos 2x and e³ up to and including the term in x³. I (b)…

A: Maclaurin Series for f(x) :       f(x)≈ f(0) +f'(0)x +f''(0)x22!+f'''(0)x33!+... Note : As per our…

Q: Decompose A into QR. A = 7 - 1 Determine the following: 92 = %3D 9 2 "12 = "21 22 Instructions for…

A:

Q: The series 3i+ 6i+ 9i+ 12i+... diverges because

A:

Q: 13.5.3 Write a in the form a = a-T+aNN at the given value of t without finding T and N. r(t) = (t+…

A: To write a in form of a=aTT+anN  given r(t)=(t+5)i+(-2t)j+t²k, t=-1

Q: 3. Let w = 3-3i and z= -2+2√3i. (a) Express w and z in polar exponential form. (b) Express (wz)10 in…

A: The given complex numbers, w=3-3i and z=-2+23i To find w and z in polar exponential form.

Q: 1. Find one real root of g (x) = ln(x*) = 0.70 between 1 and 2. How many number of iterations were…

A:

Q: Let w e C with w3 = -V3+ i. Determine all solutions w of the equation. Be sure to make the necessary…

A: Given,      w3=-3+ior, w  =-3+i13or, w  =2-32+i1213Now for θ=5π6cos 5π6=-32  and sin 5π6=12or, w…

Q: (7.5) Find all exact solutions to the equation 2sin(30 ) + 1 = 0 on the interval [0, 2n).

A: We have to find all exact solutions to the equation 2sin3θ+1=0 on the interval [0,2π).

Q: Q./ Prove( in detail) the solution of (bn) in fourier series is ( -4n / n)

A:

Q: 29. Solve the following system of equations. Give exact solutions, not decimal approximations! S In…

A: To solve the given logarithmic equation.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: