Question

the impedance in one part of a series circuit is 1+3j ohms and the impedance in another part of the circuit is 7-5j ohms. Add these complex numbers to find the total impedance in the circuit.

Answer 1

To find the total impedance in the series circuit, you simply add the two complex impedances together. The impedances given are:

1. \( Z_1 = 1 + 3j \) ohms
2. \( Z_2 = 7 - 5j \) ohms

Now, we can add them:

\[
Z_{\text{total}} = Z_1 + Z_2 = (1 + 3j) + (7 - 5j)
\]

Combine the real parts and the imaginary parts:

Real part:
\[
1 + 7 = 8
\]

Imaginary part:
\[
3j - 5j = -2j
\]

Putting it all together, we get:

\[
Z_{\text{total}} = 8 - 2j \text{ ohms}
\]

So, the total impedance in the circuit is \( 8 - 2j \) ohms.