What is (-18+16i)/(-4+10i) ?

The solution to (-18+16i)/(-4+10i) is 2+i

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simplify (-18+16i)/(-4+10i)

simplify

\frac{- 18 + 16 i}{- 4 + 10 i}

2 + i

Solution steps

\frac{- 18 + 16 i}{- 4 + 10 i}

Multiply by the conjugate

\frac{- 4 - 10 i}{- 4 - 10 i}

= \frac{( - 18 + 16 i ) ( - 4 - 10 i )}{( - 4 + 10 i ) ( - 4 - 10 i )}

Simplify

\frac{( - 18 + 16 i ) ( - 4 - 10 i )}{( - 4 + 10 i ) ( - 4 - 10 i )} : \frac{232 + 116 i}{116}

= \frac{232 + 116 i}{116}

Apply the fraction rule:

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

= \frac{232}{116} + \frac{116}{116} i

Simplify

\frac{232}{116} + \frac{116}{116} i : 2 + i

= 2 + i

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