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Problem 4. (5 points each question). Given two complex numbers Zi and Z2 in the polar...
10p Find complex numbers t = Z1 + Z2 and s-Z1-72, both in polar form, for each of the following pairs 3, b. Z1 3<30° and Z2 3-150
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
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 =
Problem 2: Total Impedance (25 Points) n electric circuit consists of two components as shown in the figure below. The values of the impedance of the two components are Zi-Ri + M and Z2-R2-JXc, wh XL 100 Ω, R2-50 Ω, and Xc-125 Ω. 21 and Z2 as complex numbers in both their rectangular and polar forms. mine the complex conjugate of Z2 and compute the product of Z222 a) Write Z1Z2 Compute the total impedance of the two components- result...
2. (a) Express each of the following complex numbers in polar form (i) i ( ii) /3 - 3i (iii) -3-V3i 42 b) For each of the complex numbers in part (a), id and
Question 3.1 (10 marks) Consider the two complex numbers-V3+i and 2 3 cis(-/3) a) Write 1V3+i in polar form, in terms of its principal argument. b) Use your answer in a) to evaluate z1/21 in polar form, and then convert that into cartesian form. c) Using their polar forms, determine z122 and z2/句in terms of their principal argument. d) Determine (22)2 in polar form, in terms of its principal argument. e) Determine all distinct values of (22)1/3 in polar form,...
Problem 3 (8 points) (a)Find the natural response and the COMPLEX forced response (2 points). (b) And then write the general REAL solution of the given differential equation (2 points). (c)Rewrite the forced response in POLAR form and sketch it on (y, t) AND on the PHASE (v, y) plane (3 points). (d) Sketch the solution of the INITIAL VALUE Problem y(0) 0, y (0) 0 using your sketches on both planes in part (c) (1 point) Use COMPLEX numbers!...
Questions. (20 pts.) a) Find the real part and imaginary part of the following complex numbers 1. jel- 2. (1 - 0260 3. b) Find polar form of the following numbers 31-3 9 Question 2. (20 pts.) a) Simplify (2< (5/7) (2<(")) 2 < (-1/6) b) Solve z+ + Z2 + 1 = 0
Problem 4 A complex number (w) is given as a function of the variable w as 2+ jw X(w) = 3 + j4w (a) Express X(w) in rectangular form and find real and imaginary parts (a) Express X(w) in polar form, and find its magnitude X(w) and its angle.
3. Find the polar form of each given complex number and sketch its position in the complex plane. a) 2-4 b) z 4i c) 2-1-i