Answer
$31 + 14i$
Work Step by Step
We get rid of the parentheses by multiplying the terms within them according to the FOIL method, meaning we multiply the first terms first, then the outer, then the inner, and, finally, the last terms:
$=(2)(8) + (2)(-5i) + (3i)(8) + (3i)(-5i)$
Multiply to simplify:
$=16 - 10i + 24i - 15i^2$
Combine like terms:
$=16 + 14i - 15i^2$
We know that the value of $i^2$ is $-1$, so we replace $i^2$ with $-1$:
$=16 + 14i - 15(-1)\\
=16+14i+15$
Group like terms:
$=(16 + 15) + 14i$
Combine like terms:
$=31 + 14i$