What is (8+19i)/(4-3i) ?

The solution to (8+19i)/(4-3i) is -1+4i

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simplify (8+19i)/(4-3i)

simplify

\frac{8 + 19 i}{4 - 3 i}

- 1 + 4 i

Solution steps

\frac{8 + 19 i}{4 - 3 i}

Multiply by the conjugate

\frac{4 + 3 i}{4 + 3 i}

= \frac{( 8 + 19 i ) ( 4 + 3 i )}{( 4 - 3 i ) ( 4 + 3 i )}

Simplify

\frac{( 8 + 19 i ) ( 4 + 3 i )}{( 4 - 3 i ) ( 4 + 3 i )} : \frac{- 25 + 100 i}{25}

= \frac{- 25 + 100 i}{25}

Apply the fraction rule:

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

= \frac{- 25}{25} + \frac{100}{25} i

Simplify

\frac{- 25}{25} + \frac{100}{25} i : - 1 + 4 i

= - 1 + 4 i

8 + 11

8 + 2 i

81 - 4

20 + 20

\frac{( 5 x y - 8 x ^{2} )}{x}