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

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Answer 1 · 2017-01-04T13:10:58

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

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.