What is (-1+8i)/(-7+7i) ?

The solution to (-1+8i)/(-7+7i) is 9/14-1/2 i

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simplify (-1+8i)/(-7+7i)

simplify

\frac{- 1 + 8 i}{- 7 + 7 i}

\frac{9}{14} - \frac{1}{2} i

Solution steps

\frac{- 1 + 8 i}{- 7 + 7 i}

Multiply by the conjugate

\frac{- 7 - 7 i}{- 7 - 7 i}

= \frac{( - 1 + 8 i ) ( - 7 - 7 i )}{( - 7 + 7 i ) ( - 7 - 7 i )}

Simplify

\frac{( - 1 + 8 i ) ( - 7 - 7 i )}{( - 7 + 7 i ) ( - 7 - 7 i )} : \frac{63 - 49 i}{98}

= \frac{63 - 49 i}{98}

Apply the fraction rule:

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

= \frac{63}{98} + \frac{- 49}{98} i

Simplify

\frac{63}{98} + \frac{- 49}{98} i : \frac{9}{14} - \frac{1}{2} i

= \frac{9}{14} - \frac{1}{2} i

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