Question
Multiply complex numbers: $$ \left( 1-4i \right) \cdot \left( 1-4i \right) $$
Answer
$$ \left( 1-4i \right) \cdot \left( 1-4i \right) = -15-8i $$
Explanation
To multiply complex numbers we can apply the FOIL method:
| Multiply the Firsts: | $ 1\cdot1 = 1$ |
| Multiply the Outers: | $ 1 \cdot \left( -4 i \right) = -4 \cdot i $ |
| Multiply the Inners: | $ -4 i \cdot 1 = -4 \cdot i $ |
| Multiply the Lasts: | $ \left( -4 i \right) \cdot \left( -4 i\right) = 16 i^2 = 16 \cdot (-1) = -16 $ |
Now we add all products together:
$$ z_1 \cdot z_2 = 1 -4 i -4 i -16 = -15-8i $$This page was created using
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