What is (4-4i)/(1+3i) ?

The solution to (4-4i)/(1+3i) is -4/5-8/5 i

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simplify (4-4i)/(1+3i)

simplify

\frac{4 - 4 i}{1 + 3 i}

- \frac{4}{5} - \frac{8}{5} i

Solution steps

\frac{4 - 4 i}{1 + 3 i}

Multiply by the conjugate

\frac{1 - 3 i}{1 - 3 i}

= \frac{( 4 - 4 i ) ( 1 - 3 i )}{( 1 + 3 i ) ( 1 - 3 i )}

Simplify

\frac{( 4 - 4 i ) ( 1 - 3 i )}{( 1 + 3 i ) ( 1 - 3 i )} : \frac{- 8 - 16 i}{10}

= \frac{- 8 - 16 i}{10}

Apply the fraction rule:

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

= \frac{- 8}{10} + \frac{- 16}{10} i

Simplify

\frac{- 8}{10} + \frac{- 16}{10} i : - \frac{4}{5} - \frac{8}{5} i

= - \frac{4}{5} - \frac{8}{5} i

\frac{2 x + 4}{2 x - 16}

\frac{30 x ^{3} - 18 x ^{2}}{6 x ^{3} + 5 x ^{2}} \cdot \frac{42 x + 35}{60 x - 36}

(2 x + 3) (3 - x) - (2 x - 5) (3 - x)

(53 - 48) \cdot 12