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
○ 8 + i
○ (partially visible)

Explanation:

Step1: Substitute \( I \) and \( Z \) into the formula

We know \( E = IZ \), \( I = 3 + 2i \) and \( Z = 2 - i \). So we need to calculate \( (3 + 2i)(2 - i) \).

Step2: Expand the product using FOIL method

\[

$$\begin{align*} (3 + 2i)(2 - i)&=3\times2+3\times(-i)+2i\times2+2i\times(-i)\\ &=6 - 3i + 4i - 2i^{2} \end{align*}$$

\]

Step3: Simplify using \( i^{2}=-1 \)

Since \( i^{2}=-1 \), then \( - 2i^{2}=-2\times(-1) = 2 \). And combine like terms: \( - 3i + 4i=i \). So we have \( 6 + 2+ i=8 + i \).

Answer:

\( 8 + i \) (corresponding to the option with \( 8 + i \))