Answer
$I=8+3i$
Work Step by Step
$E=57+67i$ $;$ $Z=9+5i$
Ohm's Law is defined by the equation $E=IZ$. In this case, $I$ is unknown.
Substitute $E$ and $Z$ into Ohm's Law equation:
$57+67i=I(9+5i)$
Rearrange:
$I(9+5i)=57+67i$
Solve for $I$ by taking $9+5i$ to divide the right side:
$I=\dfrac{57+67i}{9+5i}=...$
To find $I$, evaluate the quotient indicated. Do so by multiplying the numerator and the denominator by the complex conjugate of the denominator:
$...=\dfrac{57+67i}{9+5i}\cdot\dfrac{9-5i}{9-5i}=\dfrac{(57+67i)(9-5i)}{9^{2}-(5i)^{2}}=...$
Evaluate the operations indicated:
$...=\dfrac{513-285i+603i-335i^{2}}{81-25i^{2}}=\dfrac{513+318i-335i^{2}}{81-25i^{2}}=...$
Substitute $i^{2}$ by $-1$ and simplify:
$...=\dfrac{513+318i-335(-1)}{81-25(-1)}=\dfrac{513+318i+335}{81+25}=...$
$...=\dfrac{848+318i}{106}=\dfrac{848}{106}+\dfrac{318}{106}i=8+3i$
