What is (21-3i)/(-3+9i) ?

The solution to (21-3i)/(-3+9i) is -1-2i

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simplify (21-3i)/(-3+9i)

simplify

\frac{21 - 3 i}{- 3 + 9 i}

- 1 - 2 i

Solution steps

\frac{21 - 3 i}{- 3 + 9 i}

Multiply by the conjugate

\frac{- 3 - 9 i}{- 3 - 9 i}

= \frac{( 21 - 3 i ) ( - 3 - 9 i )}{( - 3 + 9 i ) ( - 3 - 9 i )}

Simplify

\frac{( 21 - 3 i ) ( - 3 - 9 i )}{( - 3 + 9 i ) ( - 3 - 9 i )} : \frac{- 90 - 180 i}{90}

= \frac{- 90 - 180 i}{90}

Apply the fraction rule:

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

= \frac{- 90}{90} + \frac{- 180}{90} i

Simplify

\frac{- 90}{90} + \frac{- 180}{90} i : - 1 - 2 i

= - 1 - 2 i

\frac{2 x + 7}{x - 6} - \frac{x}{x ^{2} - 3 x - 18}

\frac{3}{60}

\frac{8 x}{2 x}

3 (x - 3)

(x + 10) (x^{2} - 2 x + 3)