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Question 5 Find the principle argument of z=7+-4i Question 6 Compute the imaginary part of (5+-11)^9 Question 7 Compute the real part of (-9+71)3
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.
1. if the real part of an analytic function, f(z), is given
find the imaginary part, v(x, y) and f(z) as a function of x. (step
by step)
2. Evaluate the following complex integral (step by
step)
1. If the real part of an analytic function, f(z), is given as 2 - 12 (x2 + y2)2 find the imaginary part, v(x,y), and f(z) as a function of z. 2. Evaluate the following complex integral:
A vibration can have a real part and an imaginary part. Imagining a vibration that is described by real numbers is not problematic. But how is one to imagine a vibration that is described by complex numbers? Or are complex numbers just a mathematical tool, without physical correspondence?
Which of the following definitions about light matters interaction is WRONG? (A) The imaginary part of refractive index describes the absorption of light. (B) The damping of susceptibility depends on the applied electric field. (C) The real part of the susceptibility cannot be determined from its imaginary part. (D) The resonance optical properties of dielectric materials can be added together.
find the real and imaginary part(u and v) of the complex
function lnz
a) Find the real and imaginary parts (u and v) of the complex functions: - CZ Find out whether the functions in (a) satisfy the Cauchy-Riemann equations.
Problem 1
a)
b)
Plot real part, imaginary part and absolute value of for -2st3 2. You can use MATLAB to plot the functions but show your derivations and justify your plot.
90e-190 9+j12 3. Find the imaginary part of Y- -3.6
Solve the following questions using confomal mapping from
complex analysis
7.1 Compute the images of the real and imaginary axes and (a) the lower half-plane under the map f(z) = (2+2)/(z-i), (b) the right half-plane under the map f(z) (z 1)/(z +1), (c) the left half-plane under the map f(z) = (z+ 1)/(2-1)
7.1 Compute the images of the real and imaginary axes and (a) the lower half-plane under the map f(z) = (2+2)/(z-i), (b) the right half-plane under the...
3) (10 pts) For f(2)= a) Find the real part (0) b) Find the imaginary part (V) c) Use u and v to evaluate f (x)at z = 9 - 61