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2. Consider the complex quantity H(x) Q(1 rectangular form. Assume Q = 13, H(Q) = 2)...
1(a) Find the square roots of the complex number z -3 + j4, expressing your answer in the form a + jb. Hence find the roots for the quadratic equation: x2-x(1- 0 giving your answer in the form p+ q where p is a real number and q is a complex number. I7 marks] (b) Express: 3 + in the form ω-reje (r> 0, 0 which o is real and positive. θ < 2π). Hence find the smallest value of...
Problem 1: Consider the following complex numbers: Z1 = 2 + j4 Z2 = 5e3 a) Write zi in polar form b) Write ze in rectangular form c) Plot the product of zı & z2 in the complex plane with x(0) = 0.3 Problem 2: Consider the system: dx/dt = -3x a) Solve the initial value problem b) Plot the resulting function
Theorem 2.1 Consider an IVP of the form y' + g (x)ya h(x), y(%)-yo. Assume that g(x) and h(x) are both continuous on some interval a < x < b and that a < xo < b. Then there exists a unique solution y(x) to the initial value problem that is defined on a <x<b Theorem 2.2 Consider an IVP of the form y' = f (x.y), y(xo) = yo. Assume that ftxy) andfx, y) are both continuous on a...
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Problem 2 Write in rectangular form the complex number represented by the expression 3+2+ /2–1+ 721 – sin ( + ln(1 + (29) + \n(-1 – V31)
Directions: In 7-10, determine the rectangular equation given its polar form. [7] = 9 A. x + y2 = 3 B. x + y2 = 9 C. x² + y2 = 81 D. x + y = 9 [8] r = - 179csce A. X = -179 B. x = 179 c. y = -179 D. y = 179 E. none of these [9] @ = 13 A. y =- 13 3 x B.y = c. y = -13 D....
Problem 2. (5 points each question). Convert the rectangular form of complex numbers to the polar form 1. Z_rect = -5 - 8i Z_pol = 2. Z_rect = 2 - 71 Z_pol = 3. Z_rect = -8 + 4i Z pol- 4. Z_rect = -13.22 + 7.65i Z_pol =
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1. Consider the non-Sturm-Liouville differential equation Multiply this equation by H(x). Determine H(x) such that the equation may be reduced to the standard Sturm-Liouville form: do Given a(z), 3(2), and 7(2), what are p(x), σ(x), and q(x) 2. Consider the eigenvalue problem (a) Use the result from the previous problem to put this in Sturm-Liouville form (b) Using the Rayleigh quotient, show that λ > 0. (c) Solve this equation subject to the boundary conditions and determine...
3. Complex numbers and math a) Express z=-6 8 in polar form b) Express -1 in polar form c Express z--3e in rectangular form. d) Express z-(2+j) in rectangular form. e) For the two complex numbers z, (6-j4) ad z(-2+j1) determine in polar form. f) lf z=(-84%) determine Teal! (z*)"! in polar form.
4. simplify the complex-valued expression: V3-j6 4-1) [0.1 points] give the answer in rectangular form 4-2) [0.1 points] give the answer in polar form. The angle should be between 0 and 2n.
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Consider the following nuclear reaction 13c +e 13 0 and determine the Q value or total energy released (in MeV) in Consider the following nuclear reaction N → 6C + + v and determine the Q value or total energy released (in MeV) in this process. (Let the atomic mass of 12N be 13.0057 u, the atomic mass of 1 5.4858 x 1o-4 u.) be 13.0033 u and the...