What is (8+3i)/(2-6i) ?

The solution to (8+3i)/(2-6i) is -1/20+27/20 i

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simplify (8+3i)/(2-6i)

simplify

\frac{8 + 3 i}{2 - 6 i}

- \frac{1}{20} + \frac{27}{20} i

Solution steps

\frac{8 + 3 i}{2 - 6 i}

Multiply by the conjugate

\frac{2 + 6 i}{2 + 6 i}

= \frac{( 8 + 3 i ) ( 2 + 6 i )}{( 2 - 6 i ) ( 2 + 6 i )}

Simplify

\frac{( 8 + 3 i ) ( 2 + 6 i )}{( 2 - 6 i ) ( 2 + 6 i )} : \frac{- 2 + 54 i}{40}

= \frac{- 2 + 54 i}{40}

Apply the fraction rule:

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

= \frac{- 2}{40} + \frac{54}{40} i

Simplify

\frac{- 2}{40} + \frac{54}{40} i : - \frac{1}{20} + \frac{27}{20} i

= - \frac{1}{20} + \frac{27}{20} i

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