How do you simplify #(2-2i)*(-3+3i)#?

1 Answer
Jan 4, 2017

Perform the multiplication, using the F.O.I.L. method, substitute -1 for #i^2#, and then combine like terms.

Explanation:

Multiply the F irst terms:

#(2 -2i)*(-3 + 3i) = -6#

Multiply the Outside terms:

#(2 -2i)*(-3 + 3i) = -6 + 6i#

Multiply the I nside terms:

#(2 -2i)*(-3 + 3i) = -6 + 6i + 6i#

Multiply the Last terms:

#(2 -2i)*(-3 + 3i) = -6 + 6i + 6i - 9i^2#

Substitute -1 for #i^2#:

#(2 -2i)*(-3 + 3i) = -6 + 6i + 6i - 9(-1)#

#(2 -2i)*(-3 + 3i) = -6 + 6i + 6i + 9#

Combine like terms:

#(2 -2i)*(-3 + 3i) = 3 + 12i#

I hope that this helps.