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Problem 1: Consider the following complex numbers: Z1 = 2 + j4 Z2 = 5e3 a)...
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
Problemi: Zi= 1+ja, Z2 = 2+ j4. Find 0 ZitZz ? in Rectangular form Problema: Z, = 2130° , Z = 3145° Find ① ZitZz I in polar form Zi-Z2 ☺ 3, Problem 3 z = what is the magnitude and phase ?
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)
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 =
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 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...
[8] Plot the following complex number in the complex plane, write it in "long-hand" polar form with the argument in degrees, and write it in rectangular form. 137 5 cis 18 long-hand: rectangular: 19] Simplify (2)3 + 2i)". Write and circle your answer in both r cis 0 and x + yi form. [10] Solve for the variable over C. Circle answers in r cis form. x = 641 [11] Solve for the variable over C. Circle answers in rcise...
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.
Clear and concise handwriting please with explanation. Thank you. 20. This problem should be done without any phasor voltage or current computations. In the circuit of Figure P11.20, V = 2300 Vms at 60 Hz and the following powers (in kVA) are con- sumed by various impedances and resistances: S, = 20 + 38, S, = 20 + j18, S3 = 5+j6, and S4 = 3 + j4. (a) Find I (rectangular form) and the complex power delivered by the...
(2 points) Here are several points on the complex plane: The red point represents the complex number zı = and the blue point represents the complex number Z2 = The "modulus" of a complex number z = x+iy, written [z], is the distance of that number from the origin: z) = x2 + y2. Find the modulus of zi. |zıl = 61^(1/2) We can also write a complex number z in polar coordinates (r, 6). The angle is sometimes called...