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Problemi: Zi= 1+ja, Z2 = 2+ j4. Find 0 ZitZz ? in Rectangular form Problema: Z,...
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
III) Perform the following complex number conversions (a) convert the complex number Zi- 3+j4 to polar form tb) convert the complex number Z2-4 e0 to polar and rectangular form Hint: Z2-rexponential form. form IV What are the phase relationship between the sinusoidal waveforms brelow: v=4sin (wt + 50) i 6 sin (wt + 40) (b) v 2 cos (wt 30) i 5 sin (wt60)
Let Z! = 3H4, Z2-5-2, Z,--3-12, Z4--10-j6, and Z5--6-3. 1. Calculate Z1 + Z2 in rectangular form. 2. Calculate Z1 - Z2 in rectangular form. 3. Calculate Z3 + Z4 in polar form. 4. Calculate Za - Z5 in polar form. 5. Calculate Z1Z2-Z3 in rectangular form. 6. Find ZsZ7 in polar form. 7. Find Z7Zs in rectangular form. 8. Find ZsZs+Z7 in rectangular form Reduce the following to rectangular form. 10. Z1/Z2
Problem 4. (5 points each question). Given two complex numbers Zi and Z2 in the polar form. Find the result of operation Zi+Z2 and express it in the polar form. 1. Zi= 17 2 20; Z2 = 132 -80; ZI+Z2 2. Zi 64 2 105; Z2 = 772 -150 Zi+Z2 =
(3) Express in rectangular form all complex solutions to z2+ z +3 = 0.
Ifz-I+),22-1-j, and 3=-2, calculate the magnitude and phase (in radians) of (a) zi (b) z2 (c) z3 (d) z1 +z (e) z z3 (f) z1z2 (g) t22 (h) 을 2. 21 23 21-23 Z1
Given: Z1 = 4-j1.5 ohms; Z2 = 2+j4 ohms; Z3 = 2 ohms; 24 = 3 + j5 ohms. If the four impedances are connected in parallel, find the magnitude of equivalent impedance in ohms. (No need to include the phase angle, ONLY THE MAGNITUDE)
and z2 = 1 1 + 3i 3-i a) Given that zı = find z such that z = 2 + i 4- ¿ 22 Give your answer in the form of a + bi. Hence, find the modulus and argument of z, such that -- < arg(2) < 7. (6 marks) b) Given w = = -32, i. express w in polar form. (1 marks) ii. find all the roots of 2b = -32 in the form of a...
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.
, to the rectangular form z = a + ib and b. the polar form z re a. ie Problem 2 (15 pts) Atravelingwave is described by the wave function ψ(x, t) = ea 2-bt2-2x tap b 9 sec-2 where a = 144 crn 2 and a. In which direction is it traveling? Explain b. What is the wave speed? c. Plot (x, t) over the interval 2sxs2 for t-0 and t- 3 sec. Problem 3 (15 ntel