#### Answer

$Z=12+8i$

#### Work Step by Step

$I=10+4i$ $;$ $E=88+128i$
Ohm's Law is defined by the equation $E=IZ$. In this case, $Z$ is unknown.
Substitute $I$ and $E$ into Ohm's Law equation:
$88+128i=(10+4i)Z$
Rearrange:
$(10+4i)Z=88+128i$
Solve for $Z$ by taking $10+4i$ to divide the right side:
$Z=\dfrac{88+128i}{10+4i}=...$
To find $Z$, evaluate the quotient indicated. Do so by multiplying the numerator and the denominator by the complex conjugate of the denominator:
$...=\dfrac{88+128i}{10+4i}\cdot\dfrac{10-4i}{10-4i}=\dfrac{(88+128i)(10-4i)}{10^{2}-(4i)^{2}}=...$
Evaluate the operations indicated:
$...=\dfrac{880-352i+1280i-512i^{2}}{100-16i^{2}}=\dfrac{880+928i-512i^{2}}{100-16i^{2}}=...$
Substitute $i^{2}$ by $-1$ and simplify:
$...=\dfrac{880+928i-512(-1)}{100-16(-1)}=\dfrac{880+928i+512}{100+16}=...$
$...=\dfrac{1392+928i}{116}=\dfrac{1392}{116}+\dfrac{928}{116}i=12+8i$