What is (6-2i)/(5+3i) ?

The solution to (6-2i)/(5+3i) is 12/17-14/17 i

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simplify (6-2i)/(5+3i)

simplify

\frac{6 - 2 i}{5 + 3 i}

\frac{12}{17} - \frac{14}{17} i

Solution steps

\frac{6 - 2 i}{5 + 3 i}

Multiply by the conjugate

\frac{5 - 3 i}{5 - 3 i}

= \frac{( 6 - 2 i ) ( 5 - 3 i )}{( 5 + 3 i ) ( 5 - 3 i )}

Simplify

\frac{( 6 - 2 i ) ( 5 - 3 i )}{( 5 + 3 i ) ( 5 - 3 i )} : \frac{24 - 28 i}{34}

= \frac{24 - 28 i}{34}

Apply the fraction rule:

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

= \frac{24}{34} + \frac{- 28}{34} i

Simplify

\frac{24}{34} + \frac{- 28}{34} i : \frac{12}{17} - \frac{14}{17} i

= \frac{12}{17} - \frac{14}{17} i

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