What does $\frac{2 i}{4 - 5 i}$ $(2i)/(4-5i)$ equal?

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What does $\frac{2 i}{4 - 5 i}$ $(2i)/(4-5i)$ equal?

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Answer 1 · 2015-10-24T20:31:21

$\frac{2 i}{4 - 5 i} = - \frac{10}{41} + \frac{8}{41} i$ $(2i)/(4-5i) = -10/41+8/41 i$

Explanation:

Multiply numerator and denominator by the conjugate $(4 + 5 i)$ $(4+5i)$ of the denominator and simplify...

$\frac{2 i}{4 - 5 i} = \frac{2 i (4 + 5 i)}{(4 - 5 i) (4 + 5 i)} = \frac{- 10 + 8 i}{4^{2} + 5^{2}} = \frac{- 10 + 8 i}{16 + 25} = \frac{- 10 + 8 i}{41} = - \frac{10}{41} + \frac{8}{41} i$ $(2i)/(4-5i) = (2i(4+5i))/((4-5i)(4+5i)) = (-10+8i)/(4^2+5^2) = (-10+8i)/(16+25) = (-10+8i)/41 = -10/41+8/41 i$

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What does $\frac{2 i}{4 - 5 i}$ $(2i)/(4-5i)$ equal?

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