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Q4: 3 marks each part Answer 2 parts from the following (a) Find the real and...
Show that the real and imaginary parts of the complex-valued function f(x) = cot z are...
Show that the real and imaginary parts of the complex-valued function f(x) = cot z are - sin 2.c sinh 2g u(I,y) v(x,y) = cos 2x - cosh 2y cos 2x - cosh 2y (cot 2 = 1/tan 2)
NOTE: Show all steps in your solutions. Only partial credit will be given if steps are...
NOTE: Show all steps in your solutions. Only partial credit will be given if steps are not shown though the final answer is correct. 1. Show that the real and imaginary parts of the complex-valued function f(2) = cot z are - sin 2x sinh 2 u(x, y) v(x,y) cos 2.c – cosh 2y' cos 2x - cosh 2y (cot z = 1/ tan ) [20 points)
Real and Imaginary parts. 2. [10 marks Find all solutions to the equations 2 a) (b)...
Real and Imaginary parts.
2. [10 marks Find all solutions to the equations 2 a) (b) e1. (24-1)sin(7T2) 0.
(10 pts) Calculate the following a) Find the real and imaginary parts of e 3+nj b)...
(10 pts) Calculate the following a) Find the real and imaginary parts of e 3+nj b) Find the real and imaginary parts of ez? c) Write in polar form: 1+j
QUESTION 1 (50 marks total) (-5j) - j(j+3) (j-2)' a) Find the real and imaginary parts...
QUESTION 1 (50 marks total) (-5j) - j(j+3) (j-2)' a) Find the real and imaginary parts of complex number z = |4j-31 Present this number in both polar and exponential forms. Show it on the Argand diagram. (20 marks)
NOTE: Show all steps in your solutions. Only partial credit will be given if steps are...
NOTE: Show all steps in your solutions. Only partial credit will be given if steps are not shown though the final answer is correct. 1. Show that the real and imaginary parts of the complex-valued function f(x) = cot z are sin 2.c sinh 2 u(x,y) = v(x,y) cos 2. - cosh 2y' cos 2. - cosh 2y (cot z = 1/tanz) [20 points) 2. Obtain the equilibrium points of the following system of 1st or- der ODE and classify...
Q4 please 4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find a particular solution of the equation y" +2/ +2y = sin 2x by method of...
Q4 please
4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find a particular solution of the equation y" +2/ +2y = sin 2x by method of undetermined coeficients. 4 marks] (c) Use Laplace transform to solve the initial value problem l-1, 21 0-,0)- [10 marks]
4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find...
5. Use a substitution and an integration by parts to find each of the following indef-...
5. Use a substitution and an integration by parts to find each of the following indef- inite integrals: (b) | (cos(a) sin(a) esas) de (a) / ( (32 – 7) sin(5x + 2)) de (c) / (e* cos(e=)) dt (d) dr 6. Spot the error in the following calculation: S() will use integration by parts with 1 We wish to compute dr. For this dv du 1 dar = 1. This gives us dr by parts we find dr =...
Q4. For each signal, if it is periodic, find the fundamental period T. (in seconds) and...
Q4. For each signal, if it is periodic, find the fundamental period T. (in seconds) and the fundamental frequency (in rad/s). Otherwise prove that the signal is not periodic. [1 + 1 - 2 marks) a) X(t) = cos(5t) + sin(25t) b)x() = sin 91 + + sin(61 - 7) + cos(391)
2. In each of the following, find conditions on a, b, and c (if any) such...
2. In each of the following, find conditions on a, b, and c (if any) such that the system has (i) no solution, (ii) a unique solution, and (iii) infinitely many solutions. (b) Ix-2y = 4 | 2x +y – z = a 2x +az= 6 2y +3z= b | 3x – 4y + 5z = b IX – cz = 1 [3]
Show that the real and imaginary parts of the complex-valued function f(x) = cot z are - sin 2.c sinh 2g u(I,y) v(x,y) = cos 2x - cosh 2y cos 2x - cosh 2y (cot 2 = 1/tan 2)
NOTE: Show all steps in your solutions. Only partial credit will be given if steps are not shown though the final answer is correct. 1. Show that the real and imaginary parts of the complex-valued function f(2) = cot z are - sin 2x sinh 2 u(x, y) v(x,y) cos 2.c – cosh 2y' cos 2x - cosh 2y (cot z = 1/ tan ) [20 points)
Real and Imaginary parts.
2. [10 marks Find all solutions to the equations 2 a) (b) e1. (24-1)sin(7T2) 0.
(10 pts) Calculate the following a) Find the real and imaginary parts of e 3+nj b) Find the real and imaginary parts of ez? c) Write in polar form: 1+j
QUESTION 1 (50 marks total) (-5j) - j(j+3) (j-2)' a) Find the real and imaginary parts of complex number z = |4j-31 Present this number in both polar and exponential forms. Show it on the Argand diagram. (20 marks)
NOTE: Show all steps in your solutions. Only partial credit will be given if steps are not shown though the final answer is correct. 1. Show that the real and imaginary parts of the complex-valued function f(x) = cot z are sin 2.c sinh 2 u(x,y) = v(x,y) cos 2. - cosh 2y' cos 2. - cosh 2y (cot z = 1/tanz) [20 points) 2. Obtain the equilibrium points of the following system of 1st or- der ODE and classify...
Q4 please
4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find a particular solution of the equation y" +2/ +2y = sin 2x by method of undetermined coeficients. 4 marks] (c) Use Laplace transform to solve the initial value problem l-1, 21 0-,0)- [10 marks]
4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find...
5. Use a substitution and an integration by parts to find each of the following indef- inite integrals: (b) | (cos(a) sin(a) esas) de (a) / ( (32 – 7) sin(5x + 2)) de (c) / (e* cos(e=)) dt (d) dr 6. Spot the error in the following calculation: S() will use integration by parts with 1 We wish to compute dr. For this dv du 1 dar = 1. This gives us dr by parts we find dr =...
Q4. For each signal, if it is periodic, find the fundamental period T. (in seconds) and the fundamental frequency (in rad/s). Otherwise prove that the signal is not periodic. [1 + 1 - 2 marks) a) X(t) = cos(5t) + sin(25t) b)x() = sin 91 + + sin(61 - 7) + cos(391)
2. In each of the following, find conditions on a, b, and c (if any) such that the system has (i) no solution, (ii) a unique solution, and (iii) infinitely many solutions. (b) Ix-2y = 4 | 2x +y – z = a 2x +az= 6 2y +3z= b | 3x – 4y + 5z = b IX – cz = 1 [3]
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