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

The solution to (2-3i)/(4+3i) is -1/25-18/25 i

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

simplify

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

- \frac{1}{25} - \frac{18}{25} i

Solution steps

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

Multiply by the conjugate

\frac{4 - 3 i}{4 - 3 i}

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

Simplify

\frac{( 2 - 3 i ) ( 4 - 3 i )}{( 4 + 3 i ) ( 4 - 3 i )} : \frac{- 1 - 18 i}{25}

= \frac{- 1 - 18 i}{25}

Apply the fraction rule:

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

= \frac{- 1}{25} + \frac{- 18}{25} i

Simplify

\frac{- 1}{25} + \frac{- 18}{25} i : - \frac{1}{25} - \frac{18}{25} i

= - \frac{1}{25} - \frac{18}{25} i

2 (a - 3) (a - 1) (a + 4)

\frac{1}{50}

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