Question

the voltage v of an ac circuit can be found using the formula v = iz, where i is current and z is impedance. if i = 2 - 3i amps and z = 7 + 5i ohms, determine the voltage. simplify your answer as much as possible.

v = \boxed{} volts

Explanation:

Step1: Substitute the values of \(I\) and \(Z\) into the formula \(V = IZ\)

We have \(I = 2 - 3i\) and \(Z = 7 + 5i\), so \(V=(2 - 3i)(7 + 5i)\)

Step2: Use the distributive property (FOIL method) to multiply the complex numbers

$$
LATEXBLOCK0
$$

Step3: Recall that \(i^{2}=- 1\) and simplify the expression

Since \(i^{2}=-1\), we have \(-15i^{2}=-15\times(-1) = 15\)
Then combine like - terms:

$$
LATEXBLOCK1
$$

Answer:

\(29 - 11i\)