Answer:
50
Step-by-step explanation:
[tex]\sqrt{-64}[/tex] and [tex]\sqrt{-16}[/tex] can be expressed in complex form, with [tex]\sqrt{-1}[/tex] = i
[tex]\sqrt{-64}[/tex] = [tex]\sqrt{64(-1)}[/tex] = [tex]\sqrt{64}[/tex] × [tex]\sqrt{-1}[/tex] = 8i
[tex]\sqrt{-16}[/tex] = [tex]\sqrt{16(-1)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{-1}[/tex] = 4i
the factors can then be expressed as
(6 + 8i)(3 - 4i) ← expand using FOIL
= 18 - 24i + 24i - 32i² [ i² = ([tex]\sqrt{-1}[/tex] )² = - 1 ]
= 18 - 24i + 24i + 32 ← collect like terms
= 18 + 32 + 0
= 50
