Answer
$Z=12+8i$
Work Step by Step
Plug in the given values to the formula $E=IZ$.
$88+128i=(10+4i)Z$
Divide both sides by $(10+4i)$.
$\frac{88+128i}{10+4i}=Z$
Reduce.
$\frac{44+64i}{5+2i}=Z$
Multiply by top and bottom by the complex conjugate of the denominator.
$(\frac{5-2i}{5-2i})\frac{44+64i}{5+2i}=Z$
Expand.
$\frac{220+320i-88i-128i^2}{25+10i-10i-4i^2}=Z$
Combine like terms using the fact that $i^2=-1$.
$\frac{348+232i}{29}=12+8i=Z$
$Z=12+8i$
