Download MA40: ALGEBRA II

MA40: ALGEBRA II
UNIT 4.4 – COMPLEX NUMBERS IN REAL WORLD
& QUIZ REVIEW PROBLEMS
DO NOT WRITE ON
THIS SHEET!
DO YOUR WORK ON A SEPARATE SHEET!
LIVE GREEN…Return this sheet unwritten on and undamaged!
Design a series circuit, using the components listed to the
right, that has the indicated impedance. Draw the circuit
diagram and show your calculations. Be sure to include
the alternating current power source.
Component
Symbol
Resistor
1) Impedance = 8  i
Inductor
2) Impedance = 4  5i
Capacitor
z
4
4Ω
6i
6Ω
- 7i
7Ω
3) Impedance = 8  8i
AC Power
Source
4) The impedance in one part of a series circuit is 3  4i ohms, and the impedance in another part of
the circuit is 2  6i ohms. Add these complex numbers to find the total impedance in the circuit.
5) The current in one part of a series circuit is 4  i amps. The current in another part of the circuit is
6  4i amps. Add these complex numbers to find the total current in the circuit.
For problems #2 & #3: In an AC circuit, the voltage E , current I , and the impedance Z are all
related by the formula E  I  Z .
6) Find the voltage in a circuit if the current is 2  5i amps, and the impedance is 4  i ohms.
7) Find the current in a circuit if the voltage is 14  8i volts, and the impedance is 2  3i ohms.
For problems #8-13, simplify the expression
8)
 144
9)
 162
10)
11)
 100a 4 b 2
12)
 13   26
13)
 64x 4
10 
 
 9  2   25
For problems #14-17, write the complex number in standard form
14)  2i 5i 
15)
9  4i 2
16)
 2  5i
3i
17)
 7  4i
2  8i
OVER 

For problems #18-21, find the absolute value of each complex number and graph on the
complex plane.
19) 2i
20)
2  2i
21)
 1 4i
22)
4
For problems #22-24, find the values of m and n that make each equation true.
22) m  1  3ni  5  9i
23)
2m  5  1  ni  2  4i
24)
4  n  3m  7i  8  2i