Question
Multiply complex numbers: $$ \left( 3-2i \right) \cdot \left( -2-i \right) $$
Answer
$$ \left( 3-2i \right) \cdot \left( -2-i \right) = -8+i $$
Explanation
To multiply complex numbers we can apply the FOIL method:
| Multiply the Firsts: | $ 3\cdot\left(-2\right) = -6$ |
| Multiply the Outers: | $ 3 \cdot \left( -1 i \right) = -3 \cdot i $ |
| Multiply the Inners: | $ -2 i \cdot \left( -2 \right) = 4 \cdot i $ |
| Multiply the Lasts: | $ \left( -2 i \right) \cdot \left( -1 i\right) = 2 i^2 = 2 \cdot (-1) = -2 $ |
Now we add all products together:
$$ z_1 \cdot z_2 = -6 -3 i + 4 i -2 = -8+i $$This page was created using
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