complex numbers are used in electronics to describe the current in an electric circuit. ohms law relates the current in a circuit, i, in amperes, the voltage of the circuit, e, in volts, and the resistance of the circuit, r, in ohms, by the formula ( e = ir ). use this formula to solve the following. find e, the voltage of the circuit, if ( i = (-2 - 3i) ) amperes and ( r = (9 + 3i) ) ohms.
( e = square )
(simplify your answer. type your answer in the form ( a + bi ).)

Question

Accepted Answer

# Explanation:
## Step1: Substitute the values of $I$ and $R$ into the formula $E = IR$
Given $I=-2 - 3i$ and $R = 9+3i$, then $E=(-2 - 3i)(9 + 3i)$
## Step2: Use the distributive property (FOIL method)
$$
\begin{align*}
E&=(-2)\times(9)+(-2)\times(3i)+(-3i)\times(9)+(-3i)\times(3i)\
&=-18-6i-27i - 9i^{2}
\end{align*}
$$
## Step3: Simplify using $i^{2}=-1$
Since $i^{2}=-1$, we have $E=-18-6i - 27i-9\times(-1)$
$$
\begin{align*}
E&=-18 + 9-(6i + 27i)\
&=-9-33i
\end{align*}
$$

# Answer:
$-9-33i$

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QUESTION IMAGE

Question

Explanation:

Step1: Substitute the values of \(I\) and \(R\) into the formula \(E = IR\)

Step2: Use the distributive property (FOIL method)

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

Answer: