1. (a) Given two complex numbers z₁ = 1-√3j and 22 = 1+j, do the following: (i) Plot zi and Z2 in a cartesian plane by-hand on your answer sheet. Mark the horizontal and vertical axes with appropriate scales. (2 marks) (ii) Find the amplitude and the phase (in radians) of z₁ and 22, hence express z₁ and 22 in exponential form. (6 marks) (iii) Use the exponential forms obtained in (ii) to calculate 31 (6 marks)

Q: XP (A y dx + B x dy) + y (Cy dx + D x dy) = 0 where AD-BC # 0. xmyn,

A: Introduction: Integrating factor is related to first order ordinary differential equation. We…

Q: D2 SOLVE STEP BY STEP IN DIGITAL FORMAT Consider a metal sphere that initially has a radius of 7…

A:

Q: i need the answer quickly Q6: Find the inverse F.T of the : Ans. f(t) = e(t-2) u(t) Ans. h(t) =…

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

Q: (d) Suppose y is a least squares solution to Cx = d (for some matrix C and vector d). Show that d-Cy…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: 1 lal - If F(p) is the Fourier transform of f(x), then F(p/a) is the Fourier

A:

Q: Consider the following functions: Exercises f₁(x) = sin(x1) cos(x2), x=R² T f2(x, y) = xy, x, yern…

A: Given the functions                  f1(x)=sin(x1)cos(x2), x∈ℝ2f2(x, y)=xTy,              x, y∈ℝn…

Q: 3x #3 x dy + (3x-1) y = C-³² dx Step 1: Standard Form dy + dx (3x-1) 4 x Step 2: M(x)= e P(x) =…

A:

Q: Question 7. (10 Marks) If K is a subgroup of G and N is a normal subgroup of G, prove that KnN is a…

A:

Q: 10. (a) Let f: X→Y and g: Y→ Z be functions. Show that go f: X→ Z is a function too. (b) If f: X→Y…

A: (a.) Let f:X→Y and g:Y→Z be functions. To show: g∘f:X→Z is a function. (b.) Let f:X→Y and g:Y→Z be…

Q: Find matrices P, D, and P-1 that diagonalize matrix A, where A P- D P-1 62 88 -48-68,

A: Sol:- A matrix A can be diagonalized if there exists an invertible matrix P and diagonal matrix D…

Q: Q. No. 1. Find two consecutive positive numbers such that sum of their squares is equal 221. Q.…

A:

Q: 5. Let f(x,y) = x² + xy + y² be a function on the domain D = {(x,y) € R²: 24+ y ≤8 and y ≥ 9}. a)…

A: a) Given that fx,y=x2+xy+y2 First, find critical points. fx=2x+yfy=x+2y So,…

Q: Let A,X EM, (C) such that A is positive semidefinit and AX = XA Show that A¹/2X = XA¹/2.

A: Introduction: Definite matrix is significant in studying quadratic forms. Also, in Lyapunov…

Q: Question 2. For n ≥ 1 and x € R, let fn(2) = xn n + x²n and f(x) = f(x). Let r [0, 1) and sn (r) =…

A: As per the policy, we are solving three parts. Please repost it and specify which part is to be…

Q: 29. Consider the function f: R²R: (x,y) → f(x, y) = g( Determine the gradient of f. 1 1 2x - 2y g(1…

A: please see the STEP 2 for Details

Q: Suppose that for the three elements x, u, v of a group G, x=11v=vu, u²³=e, v=e where p and q are…

A: Given: Three elements x, u, v of a group G, such that, x=uv=vu, up=e and vq=e, where p and q are…

Q: We are looking for a solution of this function : f ∶ R2 → R (x, y) → x2+ y2− 4x + 4 with…

A: Given, fx,y=x2+y2-4x+4gx,y=2x-y2-1 Now, fxx,y=2x-4fyx,y=2ygxx,y=2gyx,y=-2y Now, fxx,y=02x-4=0x=2…

Q: Find the exact volume of the solid obtained by rotating the region bounded by the given curves about…

A: We have that the region is bounded by y=x2, y=1 and is rotated about y=6 We have: The shaded region…

Q: Identify the key steps needed to prove that a sequence , CR converges to ER in the limit n → ∞.…

A:

Q: Determine the solution of the following differential equation: dy dx 11 x² + y² xy given that y(1) =…

A: Homogeneous Differential Equation: The first order differential equation dydx=f(x,y) is called…

Q: (c) Prove by induction that 3n5n² for all n € N with n ≥ 4. State clearly where you use the…

A:

Q: Find the Laplacian of U = x³y²e²x at point (1,-1, 1). O O O O 46.42 24.46 42.26 26.24

A:

Q: 100. In a topological space, which of the following statements is correct? (A) a compact set is…

A:

Q: 1. Consider Let R(A) column space of A R(A) = column space of AT, 0 1210 2511 0 372 2 493-14 by N(A)…

A: As per our guideline we can solve only first question.  Please repost for another question. Thank…

Q: Prove that for all sets A and B and nEZ, n ≥ 1, the following holds: 72 11 (a) U(A\B) = (UA) \ B;…

A:

Q: Determine it each of the following is •solutely Convergent, Conditionally convergent for divergent.…

A:

Q: Use Frobenius method to find the solution in powers of x for the differential equation: xy'' + xy'…

A:

Q: Prove the square root of five is irrational

A:

Q: Q3 (a) (b) (c) Given the function: f(t) = {4-t 0<t <2 2 < t < 4 Show whether the function f(t) is…

A:

Q: Solve the attached lower proobltmi

A: The given lines are: y=6-2x, y=3+x and y=6 We have to compute the rotating area bounded by the given…

Q: Find the inverse Laplace transform of (s² + 4) s(s² +16)

A:

Q: [4 pts] Suppose you know that A is a 4x4 matrix with rank 4. Define a matrix transformation T: R¹ R¹…

A: A matrix transformation T : Rn → Rn given by  T(x) = Ax  then A is invertible if and only if rank(A)…

Q: Verify that this is a vector set check each property(assoctive, etc): Y = (yo, y#) (xo + yo + 1, x#…

A:

Q: Manually use Bisection iterative technique with 6 iterations to find a root of vr(t) in the…

A: Given That : v(t)=.250t4+.166t3-.500t2 To Find : root of vr(t)  in the interval [0.3,0.7] and…

Q: (b) Starting with the voltage divider rule, show that the power transmission coefficient T of an RC…

A:

Q: (1-x²¹) 22-x-x+ x + 2y = 0. d²y dy dx² dx Ay

A: Given : 1-x2d2ydx2-xdydx+λy=0 To Find : write given equation in form of Sturm-Liouville problem

Q: Let f be the function graphed below. If six subintervals of equal length are used, draw rectangles…

A:

Q: what is the Fourier transfrom of the following 0.5 d²x(t) j2nf dt2

A: In this question, the concept of Fourier Transform is applied. Fourier Transform The Fourier…

Q: SOLVE BY LIMIT DEFINITION 3x+1 2-x a) limx-2+1 limx→

A: Solution

Q: Find the laplace transformation of the following function :- f(t) = Sint + i (il 000 1 f(t) = f(t) =…

A:

Q: Use Frobenius method to find the solution in powers of x for the differential equation: xy'' + xy'…

A:

Q: Solve (y³ + 2y² +9y+18) dx = (5x²y² x²y + 17x²) dy

A:

Q: A donur Store sells hom donuts without holes. For out of к boxes of donuts n donuts and donuts of…

A:

Q: A vector field is given as G = (1/(√x² + xy))(e¯²ax +xzay), find the unit vector which is normal to…

A: The given vector fields are: G=1x2+xye-zax+xzayP=3x2ax-4yay We have to find the unit vector which is…

Q: Verify that this is a vector set check each property(assoctive, etc): X = (x0, x#) Y = (yo, y#) X+Y…

A:

Q: Calculate the Fourier series of function f(x)=x^2 -L<x<L using the Fourier series of function…

A:

Q: Which arrow correctly fills in the blank in the logical statements below? A. B. C. A. A. C. C. B. B.…

A:

Q: nits including the complet TAL FORMAT INITION

A: Value of limit is infinite

Q: f: X → Y and g: Y→ V be bijective functions. Show the following: ) gof: X → V is injective. gof: X→V…

A: It is given that f:X→Y and g:Y→V are bijective functions.

Q: Suppose an n=1 IM8 IM IM8 Consider the two series n=1 - n=1 1 5n and bn ∞ n=1 an converges and an…

A: