# How do you multiply  (5-12i)(2+3i)  in trigonometric form?

Nov 20, 2016

$= 46 - 19 i$

#### Explanation:

Expanding these factors is determined by applying Distributive property.
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Distributive Property:
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$\textcolor{b l u e}{\left(a + b\right) \left(c + d\right) = a \times c + a \times d + b \times c + b \times d}$
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$\left(5 - 12 i\right) \left(2 + 3 i\right)$
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$= \textcolor{b l u e}{5 \times 2 + 5 \times 3 i + \left(- 12 i\right) \times 2 + \left(- 12 i \times 3 i\right)}$
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$= 10 + 5 i - 24 i - 36 {i}^{2}$
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$= 10 - 19 i - 36 \times - 1 \text{ }$As we know $\text{ } {i}^{2} = - 1$
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$= 10 - 19 i + 36$
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$= 46 - 19 i$