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.
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 =
complex numbers son a) Express Z as a complex number in rectangular form. Z = (5 + 12j).(12 + 5j). e 10 b) Express Z as a complex number in polar form. 2+2+2245° 2=2-2j c) Solve for R and L, where R and L are both real numbers: 200296 + 100Li 102360R
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 ?
a) The origin in polar or cylindrical coordinates as compared to the rectangular coordinate system ______________________ A. is fixed. B. none C. follows particle. D. is body centered. b) If r = q 2 and q = 2t, find the magnitude of r and q when t = 2 seconds. A. 4 cm/sec, 2 rad/sec2 B. 8 cm/sec, 16 rad/sec2 C. 16 cm/sec, 0 rad/sec2 D. 4 cm/sec, 0 rad/sec2 c) Cylindrical or polar coordinates are a suitable choice for...
for the circuit below: a. Circuit Impedance in polar and rectangular form. b. Is the circuit more inductive or more capacitive? c. Draw the impedance phasor diagram. d. The net reactance that will make the impedance magnitude equal to 100 ohms. e. Itot, VR, VL, and VC in polar form. f. Draw the voltage phasor diagram. 47 2 80 2 35 22 4_ov frequency is 5KHz:
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....
Question 3 (a) Write the following complex numbers z + iy in polar form z+ iy re giving the angle θ as the sum of its principal argument, (chosen to lie in-r < θ,-r) and an integer multiple of 2π. That is, write θ as θ θp + 2km where k-0, 1, 2, +2Tk +2T k +2T (b) Compute all three values of i1/S and write your answers in the form a + iy.
b) r = 4 sin 8. 7. Convert each of the following equations from rectangular form to polar form. Solve for r. a) X = 3 b) x2 + (y + 2)2 = 4.
The polar form of a complex number z = a+bi is z = r(cosθ+isinθ) , where r = |z| = sqrt(a^2+b^2) , a = rcosθ and b = rsinθ and θ = tan^−1(b/a) for a > 0 and θ = tan^−1(b/a ) + π or θ = tan^−1(b/a) +180° for a < 0. What is the value for θ = tan^−1(b/a) for a = 0? Example: Express z = 0 + i in polar from with the principal argument. The...