Real and Imaginary parts. 3. [10 marks. Evaulate Ση--n eln. and deduce that sin( (n0) sin
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)
Q4: 3 marks each part Answer 2 parts from the following (a) Find the real and imaginary parts of each side of 1+a ei + az ezi® + ... = (1 - a el®)-1 (b) 2 Show that sin z cosh 2y-cos 2x (C) 1 Find the residues of at all its poles. e2z-ez
I 5) (10 pts) Calculate the following a) Find the real and imaginary parts of e8**) b) Find the real and imaginary parts of c) Write in polar form: 1+1
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)
Q1. Let x(n) be a complex values sequence with real part xr(n) and the imaginary part xi(n). Prove the following z-transform two relations: XR(2) 4 Z [ZR(n)] = _X(z) + X* (z*) 2 and X (2) - X* (*) X1() = Z XI(n) = - 2 Must you use only MATLAB in your proof, and for x(n), use two random sequences for real and the imaginary parts.
Find the real and imaginary parts of the following (a) 3 /2 (b)c- (c) e3+12 (d)e-0-) (e)j
could use some help on these, will rate! Find the real and imaginary parts of (2ei)' b) z= (2+3i)3 Problem 1.29 a) z= Problem 1.25 Light from a helium-neon laser has a wavelength of 633 nm and a wave speed of 3.00 x 10 m/s. Find the frequency, period, angular frequency, and wave number for this light.
if the input signal power is 1 W, calculate the variance of the real and imaginary parts of the Gaussian noise that needs to be added to produce: SNR = 3 dB and 10 dB (for BPSK).