What is ((2-3i))/((5+4i)) ?

The solution to ((2-3i))/((5+4i)) is -2/41-23/41 i

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simplify ((2-3i))/((5+4i))

simplify

\frac{( 2 - 3 i )}{( 5 + 4 i )}

- \frac{2}{41} - \frac{23}{41} i

Solution steps

\frac{2 - 3 i}{5 + 4 i}

Multiply by the conjugate

\frac{5 - 4 i}{5 - 4 i}

= \frac{( 2 - 3 i ) ( 5 - 4 i )}{( 5 + 4 i ) ( 5 - 4 i )}

Simplify

\frac{( 2 - 3 i ) ( 5 - 4 i )}{( 5 + 4 i ) ( 5 - 4 i )} : \frac{- 2 - 23 i}{41}

= \frac{- 2 - 23 i}{41}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{- 2}{41} + \frac{- 23}{41} i

Simplify

\frac{- 2}{41} + \frac{- 23}{41} i : - \frac{2}{41} - \frac{23}{41} i

= - \frac{2}{41} - \frac{23}{41} i

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