# How do you multiply -2i(3-7i)(4+2i)?

Sep 4, 2016

$\left(- 2 i\right) \left(3 - 7 i\right) \left(4 + 2 i\right) = - 44 - 52 i$

#### Explanation:

While multiplying complex numbers we should always remember that ${i}^{2} = - 1$.

Hence, $\left(- 2 i\right) \left(3 - 7 i\right) \left(4 + 2 i\right)$

= ((-2i×3)-2i×(-7i))(4+2i)

= $\left(- 6 i + 14 {i}^{2}\right) \left(4 + 2 i\right)$

= (-6i+14×(-1))(4+2i)

= $\left(- 14 - 6 i\right) \left(4 + 2 i\right)$

= -14×4-14×2i-6i×4-6i×2i

= -56-28i-24i-12×(-1)

= $- 56 - 28 i - 24 i + 12$

= $- 44 - 52 i$
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