What is (7+3i)/(-2+6i) ?

The solution to (7+3i)/(-2+6i) is 1/10-6/5 i

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simplify (7+3i)/(-2+6i)

simplify

\frac{7 + 3 i}{- 2 + 6 i}

\frac{1}{10} - \frac{6}{5} i

Solution steps

\frac{7 + 3 i}{- 2 + 6 i}

Multiply by the conjugate

\frac{- 2 - 6 i}{- 2 - 6 i}

= \frac{( 7 + 3 i ) ( - 2 - 6 i )}{( - 2 + 6 i ) ( - 2 - 6 i )}

Simplify

\frac{( 7 + 3 i ) ( - 2 - 6 i )}{( - 2 + 6 i ) ( - 2 - 6 i )} : \frac{4 - 48 i}{40}

= \frac{4 - 48 i}{40}

Apply the fraction rule:

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

= \frac{4}{40} + \frac{- 48}{40} i

Simplify

\frac{4}{40} + \frac{- 48}{40} i : \frac{1}{10} - \frac{6}{5} i

= \frac{1}{10} - \frac{6}{5} i

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