What is (7-3i)/(3+9i) ?

The solution to (7-3i)/(3+9i) is -1/15-4/5 i

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simplify (7-3i)/(3+9i)

simplify

\frac{7 - 3 i}{3 + 9 i}

- \frac{1}{15} - \frac{4}{5} i

Solution steps

\frac{7 - 3 i}{3 + 9 i}

Multiply by the conjugate

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

= \frac{( 7 - 3 i ) ( 3 - 9 i )}{( 3 + 9 i ) ( 3 - 9 i )}

Simplify

\frac{( 7 - 3 i ) ( 3 - 9 i )}{( 3 + 9 i ) ( 3 - 9 i )} : \frac{- 6 - 72 i}{90}

= \frac{- 6 - 72 i}{90}

Apply the fraction rule:

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

= \frac{- 6}{90} + \frac{- 72}{90} i

Simplify

\frac{- 6}{90} + \frac{- 72}{90} i : - \frac{1}{15} - \frac{4}{5} i

= - \frac{1}{15} - \frac{4}{5} i

(\frac{2 x ^{- 3}}{x y ^{2}})^{- 2}

\frac{- 28}{- 4}

(6 - x) (2 + x)

\frac{\frac{1}{x + 1} - 1}{x}

i^{- 35}