Question
Multiply complex numbers: $$ 1 \cdot \left( \frac{ 21897 }{ 10000 }+\frac{ 135617 }{ 10000 }i \right) $$
Answer
$$ 1 \cdot \left( \dfrac{ 21897 }{ 10000 }+\dfrac{ 135617 }{ 10000 }i \right) = \dfrac{ 21897 }{ 10000 }+\dfrac{ 135617 }{ 10000 }i $$
Explanation
To multiply complex numbers we can apply the FOIL method:
| Multiply the Firsts: | $ 1\cdot\frac{ 21897 }{ 10000 } = \frac{ 21897 }{ 10000 }$ |
| Multiply the Outers: | $ 1 \cdot \frac{ 135617 }{ 10000 } i = \frac{ 135617 }{ 10000 } \cdot i $ |
| Multiply the Inners: | $ 0 i \cdot \frac{ 21897 }{ 10000 } = 0 \cdot i $ |
| Multiply the Lasts: | $ \left( 0 i \right) \cdot \left( \frac{ 135617 }{ 10000 } i\right) = 0 i^2 = 0 \cdot (-1) = 0 $ |
Now we add all products together:
$$ z_1 \cdot z_2 = \frac{ 21897 }{ 10000 } + \frac{ 135617 }{ 10000 } i + 0 i + 0 = \frac{ 21897 }{ 10000 }+\frac{ 135617 }{ 10000 }i $$This page was created using
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