化简 (-5z^2-10iz+6)/((z+i)^3)+8

解答

化简

\frac{- 5 z ^{2} - 10 i z + 6}{( z + i ) ^{3}} + 8

\frac{( 8 z ^{3} - 24 z - 5 z ^{2} + 6 ) + ( 24 z ^{2} - 8 - 10 z ) i}{( z + i ) ^{3}}

求解步骤

\frac{- 5 z ^{2} - 10 i z + 6}{( z + i ) ^{3}} + 8

使用分式法则:

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

= \frac{8 ( z + i ) ^{3} - 5 z ^{2} - 10 i z + 6}{( z + i ) ^{3}}

化简

8 (z + i)^{3} - 5 z^{2} - 10 i z + 6 : 8 z^{3} + 24 z^{2} i - 24 z - 8 i - 5 z^{2} - 10 z i + 6

= \frac{8 z ^{3} + 24 z ^{2} i - 24 z - 8 i - 5 z ^{2} - 10 z i + 6}{( z + i ) ^{3}}

Rewrite in standard complex form:

\frac{( 8 z ^{3} - 24 z - 5 z ^{2} + 6 ) + ( 24 z ^{2} - 8 - 10 z ) i}{( z + i ) ^{3}}

= \frac{( 8 z ^{3} - 24 z - 5 z ^{2} + 6 ) + ( 24 z ^{2} - 8 - 10 z ) i}{( z + i ) ^{3}}

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