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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 ni 2 4i 24) 4 n 3m 7i 8 2i