化简 (-7+19i)/(4-5i)

解答

化简

\frac{- 7 + 19 i}{4 - 5 i}

- 3 + i

求解步骤

\frac{- 7 + 19 i}{4 - 5 i}

乘以共轭根式

\frac{4 + 5 i}{4 + 5 i}

= \frac{( - 7 + 19 i ) ( 4 + 5 i )}{( 4 - 5 i ) ( 4 + 5 i )}

化简

\frac{( - 7 + 19 i ) ( 4 + 5 i )}{( 4 - 5 i ) ( 4 + 5 i )} : \frac{- 123 + 41 i}{41}

= \frac{- 123 + 41 i}{41}

使用分式法则:

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

= \frac{- 123}{41} + \frac{41}{41} i

化简

\frac{- 123}{41} + \frac{41}{41} i : - 3 + i

= - 3 + i

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