Question

the relationship between voltage, e, current, i, and resistance, z, is given by the equation e = iz. if a circuit has a current i = 3 + 2i and a resistance z = 2 - i, what is the voltage of the circuit?
○ 4 - i
○ 4 + i
○ 6 + i
○ 8 + 7i

Explanation:

Step1: Substitute I and Z into E=IZ

We know \( I = 3 + 2i \) and \( Z = 2 - i \), so substitute them into \( E=IZ \), we get \( E=(3 + 2i)(2 - i) \).

Step2: Expand the product

Using the distributive property (FOIL method):

$$
LATEXBLOCK0
$$

Since \( i^{2}=- 1 \), then \( - 2i^{2}=-2\times(-1) = 2 \).

Step3: Combine like terms

Combine the real parts and the imaginary parts:

$$
LATEXBLOCK1
$$

Answer:

\( 8 + i \) (assuming the last option has a typo and should be \( 8 + i \) instead of \( 8 + 7i \))