What is (-1+5i)/(5+3i) ?

The solution to (-1+5i)/(5+3i) is 5/17+14/17 i

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simplify (-1+5i)/(5+3i)

simplify

\frac{- 1 + 5 i}{5 + 3 i}

\frac{5}{17} + \frac{14}{17} i

Solution steps

\frac{- 1 + 5 i}{5 + 3 i}

Multiply by the conjugate

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

= \frac{( - 1 + 5 i ) ( 5 - 3 i )}{( 5 + 3 i ) ( 5 - 3 i )}

Simplify

\frac{( - 1 + 5 i ) ( 5 - 3 i )}{( 5 + 3 i ) ( 5 - 3 i )} : \frac{10 + 28 i}{34}

= \frac{10 + 28 i}{34}

Apply the fraction rule:

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

= \frac{10}{34} + \frac{28}{34} i

Simplify

\frac{10}{34} + \frac{28}{34} i : \frac{5}{17} + \frac{14}{17} i

= \frac{5}{17} + \frac{14}{17} i

30 - 8

33 - 9

36 + 5

6 - 20