Angela 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 \( 3+j 4 \) amps and a resistance of \( 4-j 6 \) ohms. What is the voltage of the circuit? \begin{tabular}{l}\( -12+j 34 \) volts \\ \( -12-j 2 \) volts \\ \( 36+j 34 \) volts \\ \( 36-j 2 \) volts \\ \hline\end{tabular}

To find the voltage, we can use the given formula: \[ \text{voltage} = \text{current} \times \text{resistance} \] Here, the current is \( 3 + j 4 \) amps and the resistance is \( 4 - j 6 \) ohms. Let's multiply these two complex numbers. First, we can use the distributive property to expand the multiplication: \[ (3 + j 4)(4 - j 6) = 3 \cdot 4 + 3 \cdot (-j 6) + j 4 \cdot 4 + j 4 \cdot (-j 6) \] Calculating each term separately: 1. \( 3 \cdot 4 = 12 \) 2. \( 3 \cdot (-j 6) = -18j \) 3. \( j 4 \cdot 4 = 16j \) 4. \( j 4 \cdot (-j 6) = -24 \) (since \( j^2 = -1 \)) Now we can combine these results: \[ 12 - 18j + 16j - 24 = (12 - 24) + (-18j + 16j) = -12 - 2j \] Thus, the voltage of the circuit is \( -12 - 2j \) volts. So the correct answer is: \( -12 - j 2 \) volts.