Answer
The voltage of the circuit $E$ in volts is $\left( 21+i \right)$.
Work Step by Step
Consider the equation, $I=\left( 2-3i \right)$ and $R=\left( 3+5i \right)$
The voltage of the circuit in volts is,
$E=IR$
Substitute $I=\left( 2-3i \right)$ and $R=\left( 3+5i \right)$ in the formula $E=IR$.
$E=\left( 2-3i \right)\left( 3+5i \right)$
Use the FOIL method.
$\begin{align}
& E=2\cdot 3+2\cdot 5i-3i\cdot 3-3i\cdot 5i \\
& =6+10i-9i-15{{i}^{2}} \\
& =6+i-15{{i}^{2}}
\end{align}$
Replace the value ${{i}^{2}}=-1$.
$\begin{align}
& E=6+i-15\left( -1 \right) \\
& =6+15+i \\
& =21+i
\end{align}$
Therefore, the voltage of the circuit $E$ in volts is $\left( 21+i \right)$.
