展开 ((5+i)^4)/((4-3i)^4)

解答

展开

\frac{( 5 + i ) ^{4}}{( 4 - 3 i ) ^{4}}

- \frac{412132}{390625} - \frac{93024 i}{390625}

求解步骤

\frac{( 5 + i ) ^{4}}{( 4 - 3 i ) ^{4}}

(4 - 3 i)^{4} = - 527 - 336 i

= \frac{( 5 + i ) ^{4}}{( - 527 - 336 i )}

(5 + i)^{4} = 476 + 480 i

= \frac{476 + 480 i}{( - 527 - 336 i )}

使用复数算数法则:

\frac{a + bi}{c + d i} = \frac{( c - d i ) ( a + bi )}{( c - d i ) ( c + d i )} = \frac{( a c + b d ) + ( b c - a d ) i}{c ^{2} + d ^{2}}

a = 476, b = 480, c = - 527, d = - 336

= \frac{( 476 ( - 527 ) + 480 ( - 336 ) ) + ( 480 ( - 527 ) - 476 ( - 336 ) ) i}{( - 527 ) ^{2} + ( - 336 ) ^{2}}

整理后得

= \frac{- 412132 - 93024 i}{390625}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- 412132 - 93024 i}{390625} = - \frac{412132}{390625} - \frac{93024 i}{390625}

= - \frac{412132}{390625} - \frac{93024 i}{390625}

e x p an d (A x + B) e^{x}

e x p an d π (2 - 1) - 2

e x p an d, (2 x + 1) (4 x + 3)

e x p an d A (1 - e^{\frac{t}{d}})

e x p an d \frac{x ^{3} + x ^{2} + 4 x - 2}{( x ^{2} - x + 1 ) \cdot ( x ^{2} + 2 )}