How do you simplify $(-2+2i)(-1-i)(3-3i)$ ?

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Answer 1 · 2017-04-19T21:32:55

Use the F.O.I.L. method.

Given: $(-2+2i)(-1-i)(3-3i) = ?$

Let's use the F.O.I.L method on the first pair:

$(-2+2i)(-1-i)=(-2)(-1)+ (-2)(-i)+(2i)(-1)+(2i)(-i)$

$(-2+2i)(-1-i)=2+ 2i-2i-2i^2$

$(-2+2i)(-1-i)=2-2i^2$

Use $i^2=-1$ :

$(-2+2i)(-1-i)=2+2$

$(-2+2i)(-1-i)=4$

Multiply the above by the 3rd factor:

$(-2+2i)(-1-i)(3-3i) = 4(3-3i)$

$(-2+2i)(-1-i)(3-3i) = 12-12i$

How do you simplify (-2+2i)(-1-i)(3-3i)(-2+2i)(-1-i)(3-3i)?