단순화 1/((3-8i*x)^5)

해법

단순화

\frac{1}{( 3 - 8 i \cdot x ) ^{5}}

\frac{243 - 17280 x ^{2} + 61440 x ^{4}}{1073741824 x ^{10} + 754974720 x ^{8} + 212336640 x ^{6} + 29859840 x ^{4} + 2099520 x ^{2} + 59049} + \frac{3240 x - 46080 x ^{3} + 32768 x ^{5}}{1073741824 x ^{10} + 754974720 x ^{8} + 212336640 x ^{6} + 29859840 x ^{4} + 2099520 x ^{2} + 59049} i

솔루션 단계

\frac{1}{( 3 - 8 i x ) ^{5}}

(3 - 8 i x)^{5}

확장 :

243 - 3240 i x - 17280 x^{2} + 46080 i x^{3} + 61440 x^{4} - 32768 i x^{5}

= \frac{1}{243 - 3240 i x - 17280 x ^{2} + 46080 i x ^{3} + 61440 x ^{4} - 32768 i x ^{5}}

다시 쓰다

243 - 3240 i x - 17280 x^{2} + 46080 i x^{3} + 61440 x^{4} - 32768 i x^{5}

표준복합형태로:

(243 - 17280 x^{2} + 61440 x^{4}) + (- 3240 x + 46080 x^{3} - 32768 x^{5}) i

= \frac{1}{( 243 - 17280 x ^{2} + 61440 x ^{4} ) + ( - 3240 x + 46080 x ^{3} - 32768 x ^{5} ) i}

공역에 곱셈

\frac{( 243 - 17280 x ^{2} + 61440 x ^{4} ) + ( 3240 x - 46080 x ^{3} + 32768 x ^{5} ) i}{( 243 - 17280 x ^{2} + 61440 x ^{4} ) + ( 3240 x - 46080 x ^{3} + 32768 x ^{5} ) i}

= \frac{1 \cdot ( ( 243 - 17280 x ^{2} + 61440 x ^{4} ) + ( 3240 x - 46080 x ^{3} + 32768 x ^{5} ) i )}{( ( 243 - 17280 x ^{2} + 61440 x ^{4} ) + ( - 3240 x + 46080 x ^{3} - 32768 x ^{5} ) i ) ( ( 243 - 17280 x ^{2} + 61440 x ^{4} ) + ( 3240 x - 46080 x ^{3} + 32768 x ^{5} ) i )}

\frac{1 \cdot ( ( 243 - 17280 x ^{2} + 61440 x ^{4} ) + ( 3240 x - 46080 x ^{3} + 32768 x ^{5} ) i )}{( ( 243 - 17280 x ^{2} + 61440 x ^{4} ) + ( - 3240 x + 46080 x ^{3} - 32768 x ^{5} ) i ) ( ( 243 - 17280 x ^{2} + 61440 x ^{4} ) + ( 3240 x - 46080 x ^{3} + 32768 x ^{5} ) i )}

간소화하다 :

\frac{243 - 17280 x ^{2} + 61440 x ^{4} + i ( 3240 x - 46080 x ^{3} + 32768 x ^{5} )}{1073741824 x ^{10} + 754974720 x ^{8} + 212336640 x ^{6} + 29859840 x ^{4} + 2099520 x ^{2} + 59049}

= \frac{243 - 17280 x ^{2} + 61440 x ^{4} + i ( 3240 x - 46080 x ^{3} + 32768 x ^{5} )}{1073741824 x ^{10} + 754974720 x ^{8} + 212336640 x ^{6} + 29859840 x ^{4} + 2099520 x ^{2} + 59049}

표준 복합 형식으로 다시 작성:

\frac{243 - 17280 x ^{2} + 61440 x ^{4}}{1073741824 x ^{10} + 754974720 x ^{8} + 212336640 x ^{6} + 29859840 x ^{4} + 2099520 x ^{2} + 59049} + \frac{3240 x - 46080 x ^{3} + 32768 x ^{5}}{1073741824 x ^{10} + 754974720 x ^{8} + 212336640 x ^{6} + 29859840 x ^{4} + 2099520 x ^{2} + 59049} i

= \frac{243 - 17280 x ^{2} + 61440 x ^{4}}{1073741824 x ^{10} + 754974720 x ^{8} + 212336640 x ^{6} + 29859840 x ^{4} + 2099520 x ^{2} + 59049} + \frac{3240 x - 46080 x ^{3} + 32768 x ^{5}}{1073741824 x ^{10} + 754974720 x ^{8} + 212336640 x ^{6} + 29859840 x ^{4} + 2099520 x ^{2} + 59049} i