5. (a) Find all complex z satisfying 24 + 16 = 0. (b) Find the inverse...
Q1. Solve the complex equation: sinz 3i Q2. Study the analyticity of the complex function fusing Cauchy-Riemann equations: Izl Q3. Evaluate, by using Cauchy's integral formula, the path integral cosh2 z dz (z-1-i(z-4) where C consists of Iz 3 (counterclockwise) Q4. Using the Residue theorem, integrate counterclockwise around the circle C defined by zl 1.5, the following tan z dz Q5. Find, by using parti ial fraction, the Laurent series of the function with center zo 0 for 1< z<3...
(b) 10 points Find all complex numbers z satisfying 28 – 324 – 4 = 0.
Find the inverse z-transform x[n] of X(z) = (-2z+6z^2)/(-z^2+2z^3) of the first 4 values starting from 0 (z is a complex variable)
...please with good write hand (b) 10 points Find all complex numbers z satisfying 28 – 324 – 4 = 0.
If zo E C is a constant complex number, and r> 0 is constant, consider the curve in C in C parametrized by 0 according to z(0) = 20 +reio 0 € (0,27] (a) Carefully describe the nature of the curve C. (b) Using the parametrization above, compute particular attention to the dependence of your answer on the three parameters in this question: r >0, ne Z and zo E C. (c) If F(z) is such that F"(z) = (2-zo)",...
Consider the following complex-variable function cosh a < T f(z) la! cosh πχ, a) Find all its singularities, state their nature and compute the residues b) Consider the rectangular contour y with vertices at tR and tRi. Evaluate 6 6 dz cosh πχ c) Using the previous result take the limit R-to prove that cosh ax (10] 2 cos (g Hint: remember that cosh(a + b) -cosh a cosh b + sinh a sinh b d) Why is the above...
Find Z-Transform of f(k) = e-2ksinh4k , k 0 Find inverse Z-Transform of -1T-2 <Iz 5 markS ii) 2 2 (+2z Solve any three Q4A] 15 marks Is the following function even or odd? Find its Fourier series: i) 2 Find Z-Transform of f(k) = e-2ksinh4k , k 0 Find inverse Z-Transform of -1T-2
5. Suppose X has the Rayleigh density otherwise 0, a. Find the probability density function for Y-X using Theorem 8.1.1. b. Use the result in part (a) to find E() and V(). c. Write an expression to calculate E(Y) from the Rayleigh density using LOTUS. Would this be easier or harder to use than the above approach? of variables in one dimension). Let X be s Y(X), where g is differentiable and strictly incr 1 len the PDF of Y...
(b) Determine the inverse of the following matrix using elementary row operations 0 1 [ 3 C = -1 2 5 O-11VIMU (50 marks) Given the vector field F = x2i +2xj + z?k and the closed curve is a square with vertices at (0,0,3), (1, 0, 3), (1, 1, 3), and (0, 1,3), verify Stoke's Theorem (a) 5. (50 marks) Use the Gauss-Seidel iterative technique to find approximate solutions to (b) 6 +2x3 10x1 +3x4 11x2 X3 11 x4...
Based on the document below, 1. Describe the hypothesis Chaudhuri et al ids attempting to evaluate; in other words, what is the goal of this paper? Why is he writing it? 2. Does the data presented in the paper support the hypothesis stated in the introduction? Explain. 3.According to Chaudhuri, what is the potential role of thew alkaline phosphatase in the cleanup of industrial waste. CHAUDHURI et al: KINETIC BEHAVIOUR OF CALF INTESTINAL ALP WITH PNPP 8.5, 9, 9.5, 10,...