Consider A 2 3i B 5 I C 7i What is A B 2C in Cartesia

Consider A = 2 - 3i B = 5 + I C = 7i What is A = B + 2C in Cartesian notation? What is B(A+C)/A in Cartesian notation? Express B, A and (A + C) in Polar notation and repeat the above question. A 330 Ohm resistor is placed in series with a 3.20 milliFarad Capacitor What is the Magnitude of the resulting impedance, Z, (in ohms) and current I, (in amps) when it is hooked up to a 60 Hz 220 V outlet?

Solution

A = 2-3i

B = 5 + i

C = 7i

a) A - B + 2C

2- 3i - 5 - i + 14i

cartesian form is

-3 + 10i

b) B (A+C) / A

(5+i) ( 2+4i ) / 2-3i

(10 + 22i +4i^2 ) / (2 - 3i )

( 6 + 22i ) / (2-3i )

multiplying top and bottom by conjugate of denominator

( 6 + 22i )( 2+3i) / (2-3i)(2+3i)

= -54/13 + 62i / 13