What is (29-15i)/(-4-5i) ?

The solution to (29-15i)/(-4-5i) is -1+5i

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simplify (29-15i)/(-4-5i)

simplify

\frac{29 - 15 i}{- 4 - 5 i}

- 1 + 5 i

Solution steps

\frac{29 - 15 i}{- 4 - 5 i}

Multiply by the conjugate

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

= \frac{( 29 - 15 i ) ( - 4 + 5 i )}{( - 4 - 5 i ) ( - 4 + 5 i )}

Simplify

\frac{( 29 - 15 i ) ( - 4 + 5 i )}{( - 4 - 5 i ) ( - 4 + 5 i )} : \frac{- 41 + 205 i}{41}

= \frac{- 41 + 205 i}{41}

Apply the fraction rule:

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

= \frac{- 41}{41} + \frac{205}{41} i

Simplify

\frac{- 41}{41} + \frac{205}{41} i : - 1 + 5 i

= - 1 + 5 i

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