Question: Alma 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) \cdot (resistance). The circuit she tests has a current of $4 + j3$ amps and a resistance of $5 - j3$ ohms. What is the voltage of the circuit?
1. **State the problem:** We need to find the voltage of a circuit given the current $4 + j3$ amps and resistance $5 - j3$ ohms using the formula $$\text{voltage} = \text{current} \times \text{resistance}.$$
2. **Write the formula:** $$V = I \times R$$ where $I = 4 + j3$ and $R = 5 - j3$.
3. **Multiply the complex numbers:**
$$V = (4 + j3)(5 - j3)$$
Use distributive property:
$$= 4 \times 5 + 4 \times (-j3) + j3 \times 5 + j3 \times (-j3)$$
$$= 20 - j12 + j15 - j^2 9$$
4. **Simplify using $j^2 = -1$:**
$$= 20 - j12 + j15 - (-1)9$$
$$= 20 - j12 + j15 + 9$$
5. **Combine like terms:**
Real part: $20 + 9 = 29$
Imaginary part: $-j12 + j15 = j3$
6. **Final voltage:**
$$V = 29 + j3$$ volts.
7. **Answer choice:** $29 + j3$ volts.