Let Z! = 3H4, Z2-5-2, Z,--3-12, Z4--10-j6, and Z5--6-3. 1. Calculate Z1 + Z2 in rectangular form. 2. Calculate Z1 - Z2 in rectangular form. 3. Calculate Z3 + Z4 in polar form. 4. Calculate Za - Z5 in polar form. 5. Calculate Z1Z2-Z3 in rectangular form. 6. Find ZsZ7 in polar form. 7. Find Z7Zs in rectangular form. 8. Find ZsZs+Z7 in rectangular form Reduce the following to rectangular form. 10. Z1/Z2
The Hungarian algorithm: An example We consider an example where four jobs (J1, J2, J3, and J4) need to be executed by four workers (W1, W2, W3, and W4), one job per worker. The matrix below shows the cost of assigning a certain worker to a certain job. The objective is to minimize the total cost of the assignment. J1 J2 J3 J4 W1 82 83 69 92 W2 77 37 49 92 W3 11 69 5 86 W4 8...
1(a) Find the square roots of the complex number z -3 + j4, expressing your answer in the form a + jb. Hence find the roots for the quadratic equation: x2-x(1- 0 giving your answer in the form p+ q where p is a real number and q is a complex number. I7 marks] (b) Express: 3 + in the form ω-reje (r> 0, 0 which o is real and positive. θ < 2π). Hence find the smallest value of...
Solve the system. -3x+y+4z=1 x+y+z=0 -2x+z=-1 x+y-2z=0 Please show all steps! I thought I got the correct answer but my numbers don't work for the last given equation. Thank you!
For the complex number given as: z = a + bi / c+di where i = √−1 is the imaginary unit. The parameters are defined as a = √2, b = 0, c = 0.5 and d = −0.5. (a) Find the real and the imaginary parts of z, and then draw the Argand dia- gram. (Hint: Use the conjugate of the denominator.) 2.5 (b) Based on the Argand diagram, find the distance r of the complex number z from...
Show all work for credit General Solution Roots | y(z) = Genz + Cenz Two real roots r T2 One real root r Bi | y(z)-Geaz cos(ßz) + Ceaz sin(8z) Two complex roots a Form of p | Example f(t) | Example2 Form of f(t) A cos(t)+Bsin(at) 1. Find the general solution to the DE: y" +4y +4y Show all work for credit General Solution Roots | y(z) = Genz + Cenz Two real roots r T2 One real root...
SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY THE CRAMER'S METHOD 3X+5Y+3Z-12 2X+5Y-2Z-6 3x+6Y+3Z-3 a) X Y b) CHECK YOUR RESULTS. (USE MATRICE FUNCTIONS, PRESS F2. AND THEN PRESS CTRL+SHIFT+ENTER) 3IF Y-SINC) EXPOO. INTEGRATE Y FROM X-0 Tox-1. COMPARE WITH REAL VALUE IF DX-0 a) INT b) INT ,IF DX- 005 REAL VALUE 3) Plot sin x letting maco c/ Prepave hese cuves 4) SOLVE THE FOLLOWING SYSTEM OF EQUATIONS BY INVERSE METHOD 3 X+3Z-13 2X +5 Y-2Z-2 3 X+6Y+2Z-3 Z-...
(1 Consider the symmetric matrix A = 2 10 2 0 2 2 1. Answer the following questions. 2 3 (1) Find the eigenvalues , , and iz (2 <, <1z) of the matrix A and their corresponding eigenvectors. (2) Find the orthogonal matrix B and its inverse matrix B' that satisfy the following equation: (4 0 0 B-'AB = 0 0 lo o 2) (3) Suppose that the real vectors y and 9 satisfy the following relationship: Show that...
7. Let z x+y (a) Show that f(z) z3 is analytic. 4 marks Recall the Caucy-Riemann equations are: ди ди an d_ where f (z) -u(x, y) + iv(x, y). (b) Let x2 and y 1 such that z-2i is a solution to 2abi [3 marks] Determine a and b (c) Find all other solutions of 23-a + bi in polar form correct to 2 significant 3 marks] figures If you were not able to solve for a and b...
z -1 2+32 subject to x*y . Find the maximum and minimum values of f(x, y,z) x + 2y and x-y +2z + 2. z -1 2+32 subject to x*y . Find the maximum and minimum values of f(x, y,z) x + 2y and x-y +2z + 2.