Question
Multiply complex numbers: $$ \left( 1+4i \right) \cdot \left( 9+2i \right) $$
Answer
$$ \left( 1+4i \right) \cdot \left( 9+2i \right) = 1+38i $$
Explanation
To multiply complex numbers we can apply the FOIL method:
| Multiply the Firsts: | $ 1\cdot9 = 9$ |
| Multiply the Outers: | $ 1 \cdot 2 i = 2 \cdot i $ |
| Multiply the Inners: | $ 4 i \cdot 9 = 36 \cdot i $ |
| Multiply the Lasts: | $ \left( 4 i \right) \cdot \left( 2 i\right) = 8 i^2 = 8 \cdot (-1) = -8 $ |
Now we add all products together:
$$ z_1 \cdot z_2 = 9 + 2 i + 36 i -8 = 1+38i $$This page was created using
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