What is (-46+54i)/(-5-7i) ?

The solution to (-46+54i)/(-5-7i) is -2-8i

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simplify (-46+54i)/(-5-7i)

simplify

\frac{- 46 + 54 i}{- 5 - 7 i}

- 2 - 8 i

Solution steps

\frac{- 46 + 54 i}{- 5 - 7 i}

Multiply by the conjugate

\frac{- 5 + 7 i}{- 5 + 7 i}

= \frac{( - 46 + 54 i ) ( - 5 + 7 i )}{( - 5 - 7 i ) ( - 5 + 7 i )}

Simplify

\frac{( - 46 + 54 i ) ( - 5 + 7 i )}{( - 5 - 7 i ) ( - 5 + 7 i )} : \frac{- 148 - 592 i}{74}

= \frac{- 148 - 592 i}{74}

Apply the fraction rule:

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

= \frac{- 148}{74} + \frac{- 592}{74} i

Simplify

\frac{- 148}{74} + \frac{- 592}{74} i : - 2 - 8 i

= - 2 - 8 i

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\frac{12 !}{2 ! 10 !}