Question

question 26
marcia is an electrical engineer who is testing the voltage of a circuit given a certain current and resistance. she uses the following formula to calculate voltage:
voltage = (current) · (resistance)
the circuit she tests has a current of 5 + j3 amps and a resistance of 3 - j2 ohms.
what is the voltage of the circuit?
11 + j volts
21 + j volts
11 - j volts
21 - j volts

Explanation:

Step1: Multiply the two complex numbers

$$(5 + j3)(3 - j2)$$
Use the FOIL method:
First: \(5\times3 = 15\)
Outer: \(5\times(-j2)=-j10\)
Inner: \(j3\times3 = j9\)
Last: \(j3\times(-j2)=-j^{2}6\)

Step2: Simplify the expression

Combine like terms:
\(15 - j10 + j9- j^{2}6\)
Since \(j^{2}=-1\), then \(-j^{2}6 = 6\)
\(15 + 6+(-j10 + j9)\)
\(21 - j\)

Answer:

\(21 - j\) volts (the fourth option)