Problem
Complex numbers are used in electronics to describe the current in an electric circuit. Ohm's 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 $E=I R$. Find $E$, the voltage of a circuit if $I=(9-4 i)$ amperes and $R=(6+7 i)$ ohms. $E=\square$ volts (Simplify your answer. Type your answer in the form a + bi.)
Solution
Step 1 ：Given the current, I = (9-4i) amperes and the resistance, R = (6+7i) ohms in the circuit.
Step 2 ：According to Ohm's law, the voltage, E in the circuit is given by the formula E = IR.
Step 3 ：Substitute the given values of I and R into the formula.
Step 4 ：Calculate E = (9-4i) * (6+7i) = (82+39i) volts.
Step 5 ：\(\boxed{E = 82+39i}\) volts is the voltage of the circuit.
