4.9. For the complex numbers z2+j3 and z2-1 -j6, show the following:
two impedances z1=3+j6 ohms and z2=4-j3 ohms are connected in series. what is the magnitude of the resultant impedance ?
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
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
16. Given complex numbers 21 = 3 – 7i and z2 = -1+9i, find the absolute value of (3z1 + 2z2): | 3z1 + 2z2 = ? (16)
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
if the two branches of a 440v parallel circuit have the impedences z1=2-j and z2 1+j3 what is the true power in the circuit
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 =
(2) (a) Let {n}nen be a sequence of complex numbers. Show that if lim, toon = 2, then lim 21+z2+ + + Zn 100 (b) Using (a), find the limit limn7 (m_ +i i zm).
Question 2 (1 point) Consider the complex number 2 -j6. The polar form of this number is a) 6.3271.6° b) 6.32-71.6° O d) -6.3271.6° d) 402-71.6
Suppose z1, z2 and z3 are distinct points in the extended complex plane C ∗ . Show that the unique M¨obius transform taking these points to 1, 0,∞ in order is z → (z, z1, z2, z3), where (z, z1, z2, z3) is the cross ratio