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

The solution to (4+i)/(-3+2i) is -10/13-11/13 i

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

simplify

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

- \frac{10}{13} - \frac{11}{13} i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

\frac{( 4 + i ) ( - 3 - 2 i )}{( - 3 + 2 i ) ( - 3 - 2 i )} : \frac{- 10 - 11 i}{13}

= \frac{- 10 - 11 i}{13}

Apply the fraction rule:

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

= \frac{- 10}{13} + \frac{- 11}{13} i

Simplify

\frac{- 10}{13} + \frac{- 11}{13} i : - \frac{10}{13} - \frac{11}{13} i

= - \frac{10}{13} - \frac{11}{13} i

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