## Precalculus (6th Edition) Blitzer

The voltage of the circuit $E$ in volts is $\left( 47+13i \right)$.
Consider the equation, $I=\left( 4-5i \right)$ and $R=\left( 3+7i \right)$ The voltage of the circuit in volts is, $E=IR$ Substitute $I=\left( 4-5i \right)$ and $R=\left( 3+7i \right)$ in the formula$E=IR$. $E=\left( 4-5i \right)\left( 3+7i \right)$ Use the FOIL method. \begin{align} & E=4\cdot 3+4\cdot 7i-5i\cdot 3-5i\cdot 7i \\ & =12+28i-15i-35{{i}^{2}} \\ & =12+13i-35{{i}^{2}} \end{align} Replace the value ${{i}^{2}}=-1$. \begin{align} & E=12+13i-35\left( -1 \right) \\ & =12+35+13i \\ & =47+13i \end{align} Therefore, the voltage of the circuit $E$ in volts is $\left( 47+13i \right)$.