Question

if the impedance of a resistor in a circuit is $z_1 = 3 + 3i$ ohms and the impedance of a second resistor is $z_2 = 5 - i$ ohms. find the total impedance of the two resistors when they are placed in series. (use sum of the two impedances.)
the total impedance is $square$ ohms.
(simplify your answer. express complex numbers in terms of $i$.)

Explanation:

Step1: Recall impedance addition rule

When resistors are in series, total impedance $Z = Z_1+Z_2$. Given $Z_1 = 3 + 3i$ and $Z_2=5 - i$.

Step2: Add the real - parts and imaginary - parts separately

Add the real parts: $3 + 5=8$. Add the imaginary parts: $3i+( - i)=3i - i = 2i$.
So, $Z=(3 + 5)+(3i - i)=8 + 2i$.

Answer:

$8 + 2i$