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 + j4 amps and a resistance of 4 – j6 ohms.  

What is the voltage of the circuit? 

The voltage of a circuit is calculated using the formula:

\[
\text{voltage} = (\text{current}) \cdot (\text{resistance})
\]

In this case, the current is \( 3 + j4 \) amps, and the resistance is \( 4 - j6 \) ohms. Since both current and resistance are complex numbers, we need to multiply these complex numbers to find the voltage.

To multiply two complex numbers, \( (a + jb) \) and \( (c + jd) \), the result is:

\[
(a + jb) \cdot (c + jd) = (ac - bd) + j(ad + bc)
\]

Now let's apply this to the given values:

\[
(3 + j4) \cdot (4 - j6)
\]

Where:
- \( a = 3 \), \( b = 4 \)
- \( c = 4 \), \( d = -6 \)

Now we calculate:

1. Real part: \( (3 \cdot 4) - (4 \cdot -6) = 12 + 24 = 36 \)
2. Imaginary part: \( (3 \cdot -6) + (4 \cdot 4) = -18 + 16 = -2 \)

Thus, the voltage is:

\[
\text{voltage} = 36 - j2
\]

So, the voltage of the circuit is \( 36 - j2 \) volts.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How do you add or subtract complex numbers?
2. What is the physical meaning of imaginary components in electrical engineering?
3. How do you convert complex numbers to polar form?
4. How can voltage be calculated for more complex circuits?
5. What is the impedance in AC circuits, and how does it differ from resistance?

**Tip**: When multiplying complex numbers, remember to use the distributive property and keep track of the imaginary unit \( j^2 = -1 \).

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 + j4 amps and a resistance of 4 – j6 ohms. What is the voltage of the circuit?

Learn how to calculate voltage using complex numbers in an electrical circuit with current 3 + j4 amps and resistance 4 - j6 ohms. This example explains the multiplication of complex numbers using the distributive property, with a step-by-step solution ideal for high school and college-level electrical engineering students.

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