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

Question

Accepted Answer

# 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):
$$
\begin{align*}
(3 + 2i)(2 - i)&=3\times2-3\times i+2i\times2 - 2i\times i\
&=6-3i + 4i-2i^{2}
\end{align*}
$$
Since $ i^{2}=- 1 $, then $ - 2i^{2}=-2\times(-1) = 2 $.

## Step3: Combine like terms
Combine the real parts and the imaginary parts:
$$
\begin{align*}
6 + 2+(-3i + 4i)&=(6 + 2)+( - 3i+4i)\
&=8 + i
\end{align*}
$$

# Answer:
$ 8 + i $ (assuming the last option has a typo and should be $ 8 + i $ instead of $ 8 + 7i $)

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QUESTION IMAGE

Question

Explanation:

Step1: Substitute I and Z into E=IZ

Step2: Expand the product

Step3: Combine like terms

Answer: