expand the parenthesis by multiplying through, treat the imaginary number as you would any variable until the end.
(2 - 5i)(4 + 7i)
8 + 14i - 20i - 35i²
combine like terms
8 - 6i - 35i²
Now "i" represents √(-1), leave that there but...
i² = (√(-1) )² = -1
substitute -1 for i
8 - 6i - 35(-1)
8 - 6i + 35
43 - 6i
