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Complex 6. Find a branch of the multiple-valued expression f(z)-log(i(z + 21)) which is analytic for all z in the open disk
Hw2 Q1 Show that the function f(z) = z2 + z is analytic. Also find its derivative. (Hint: check CR Equations for Analyticity, and then proceed finding the derivative as shown in video 8 by any of the two rules shown in video 7] Q2 Verify that the following functions are harmonic i. u = x2 - y2 + 2x - y. ii. v=e* cos y. Q3 Verify that the given function is harmonic, and find the harmonic conjugate function...
11. Describe the branch cuts and branch points of the function (1-z2)1/2 and evaluate the real integral dx 11. Describe the branch cuts and branch points of the function (1-z2)1/2 and evaluate the real integral dx
Find I1, I2, IaA, IbB, IcC. Each source is 115 V rms. z1 = 3+j4 Z2 = 4+j3 z3 = 5+j0 Please show all work and steps. Von D I 0 van |z22 o Iz Von - Find I, I2, Tax, IOB, Icc. - Eacn source is 115 Vrms. Z = 3+34 Z2 = 4 + 8 3 Z3=5T;O
please solve these two questions completely with steps thank you! 2. Find the image of a horizontal line under the mapping w e Problem 5. Evaluate the following integrals, justifying your procedures. 1. e z, where C is the circle with radius, Centre 1,positively oriented. 2. Let CRbe the circle ll R(R> 1), described in the counterclockwise direction. Show that Log Problem 6. The function g(z) = Vre2 (r > 0,-r < θπ) is analytic in its domain of definition,...
i found 8pi(2-sqrt(2)) (5) (20 points total) The region W lies between the spheres x2y z2 1 and x2y2 + z2 9 and within the cone z22 +y2with z 2 0; its boundary is the closed surface, S, oriented outward. For G-: < x, y, z >, where -A2 + y2 + z2 . Use the divergence Theorem to computeJI, .ds (5) (20 points total) The region W lies between the spheres x2y z2 1 and x2y2 + z2 9...
5. Let f(x) = e-} Log(z) (that is, f is the principal branch of z-1/2). Compute [flade, where (a) (2 points) y is the upper half of the unit circle C(0) from +1 to -1; (b) (2 points) y is the lower half of the unit circle C1(0) from +1 to -1.
15 pts] Problem 10. 5 pts) (i) Give the formula in polar coordinates for the branch of -1/2 that is defined in the complement of the negative imaginary axis including the origin, so that (-1)-12-i. Using that branch, describe the largest domain in which the function 1/2 is analytic. 15 pts] Problem 10. 5 pts) (i) Give the formula in polar coordinates for the branch of -1/2 that is defined in the complement of the negative imaginary axis including the...
Q3: 5 marks (A) Expand f(z) (2-1)(2-3) in a Laurent series valid for (i) Iz - 11 < 2, and (ii) Iz - 31 < 2. 1.5 marks each part (B) Use Laurent series to find the residue of f(2)= e (x - 2)-2 at its pole z = 2. 2 marks
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