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)⋅(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?

To calculate the voltage \( V \) of the circuit given the current \( I \) and resistance \( R \), we use the formula:

\[ V = I \cdot R \]

Given:
- Current \( I = 4 + j3 \) amps
- Resistance \( R = 5 - j3 \) ohms

We perform the multiplication of these two complex numbers:

\[ (4 + j3) \cdot (5 - j3) \]

We use the distributive property (FOIL method) for the multiplication:

\[ (4 + j3)(5 - j3) = 4 \cdot 5 + 4 \cdot (-j3) + j3 \cdot 5 + j3 \cdot (-j3) \]

Now, calculate each term separately:

1. \( 4 \cdot 5 = 20 \)
2. \( 4 \cdot (-j3) = -j12 \)
3. \( j3 \cdot 5 = j15 \)
4. \( j3 \cdot (-j3) = -9 \) (since \( j^2 = -1 \))

Combine these results:

\[ 20 - j12 + j15 - 9 \]

Now, combine the real and imaginary parts:

- Real part: \( 20 - 9 = 11 \)
- Imaginary part: \( -j12 + j15 = j3 \)

So, the voltage \( V \) is:

\[ V = 11 + j3 \]

Thus, the voltage of the circuit is \( 11 + j3 \) volts.

Do you want more details or have any questions?

Here are 5 questions you can ask next:
1. How do I perform operations on complex numbers?
2. Can you explain the concept of impedance in AC circuits?
3. How do I convert a complex number from rectangular to polar form?
4. What is the significance of the imaginary unit \( j \) in electrical engineering?
5. Can you solve another problem involving complex numbers in electrical circuits?

Tip: When working with complex numbers in electrical engineering, always remember to separate real and imaginary parts for easier calculation and interpretation.

Learn how to calculate the voltage in electrical circuits using complex numbers. This problem involves determining the voltage given the current and resistance using the formula V = I * R, where I = 4 + j3 amps and R = 5 - j3 ohms. Follow a detailed step-by-step solution with real and imaginary parts calculation.

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