Question
Multiply complex numbers: $$ \left( 1+9i \right) \cdot \left( 3+5i \right) $$
Answer
$$ \left( 1+9i \right) \cdot \left( 3+5i \right) = -42+32i $$
Explanation
To multiply complex numbers we can apply the FOIL method:
| Multiply the Firsts: | $ 1\cdot3 = 3$ |
| Multiply the Outers: | $ 1 \cdot 5 i = 5 \cdot i $ |
| Multiply the Inners: | $ 9 i \cdot 3 = 27 \cdot i $ |
| Multiply the Lasts: | $ \left( 9 i \right) \cdot \left( 5 i\right) = 45 i^2 = 45 \cdot (-1) = -45 $ |
Now we add all products together:
$$ z_1 \cdot z_2 = 3 + 5 i + 27 i -45 = -42+32i $$This page was created using
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