What is (7-5i)/(5+9i) ?

The solution to (7-5i)/(5+9i) is -5/53-44/53 i

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simplify (7-5i)/(5+9i)

simplify

\frac{7 - 5 i}{5 + 9 i}

- \frac{5}{53} - \frac{44}{53} i

Solution steps

\frac{7 - 5 i}{5 + 9 i}

Multiply by the conjugate

\frac{5 - 9 i}{5 - 9 i}

= \frac{( 7 - 5 i ) ( 5 - 9 i )}{( 5 + 9 i ) ( 5 - 9 i )}

Simplify

\frac{( 7 - 5 i ) ( 5 - 9 i )}{( 5 + 9 i ) ( 5 - 9 i )} : \frac{- 10 - 88 i}{106}

= \frac{- 10 - 88 i}{106}

Apply the fraction rule:

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

= \frac{- 10}{106} + \frac{- 88}{106} i

Simplify

\frac{- 10}{106} + \frac{- 88}{106} i : - \frac{5}{53} - \frac{44}{53} i

= - \frac{5}{53} - \frac{44}{53} i

15 (6 - g)

(x^{2} + 3 x + 3) - (7 x^{2} - x - 1)

- 3 x + 9 x

(8 h^{2} - 7)^{2}

2 (b) + 2 (3 c)