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Phổ biến Đại số >

rút gọn 1/((7-5ix)^7)

Lời Giải

rút gọn

\frac{1}{( 7 - 5 \cdot i \cdot x ) ^{7}}

Lời Giải

\frac{823543 - 8823675 x ^{2} + 7503125 x ^{4} - 765625 x ^{6}}{6103515625 x ^{14} + 83740234375 x ^{12} + 492392578125 x ^{10} + 1608482421875 x ^{8} + 3152625546875 x ^{6} + 3707487643125 x ^{4} + 2422225260175 x ^{2} + 678223072849} + \frac{4117715 x - 10504375 x ^{3} + 3215625 x ^{5} - 78125 x ^{7}}{6103515625 x ^{14} + 83740234375 x ^{12} + 492392578125 x ^{10} + 1608482421875 x ^{8} + 3152625546875 x ^{6} + 3707487643125 x ^{4} + 2422225260175 x ^{2} + 678223072849} i

Các bước giải pháp

\frac{1}{( 7 - 5 i x ) ^{7}}

Mở rộng

(7 - 5 i x)^{7} : 823543 - 4117715 i x - 8823675 x^{2} + 10504375 i x^{3} + 7503125 x^{4} - 3215625 i x^{5} - 765625 x^{6} + 78125 i x^{7}

= \frac{1}{823543 - 4117715 i x - 8823675 x ^{2} + 10504375 i x ^{3} + 7503125 x ^{4} - 3215625 i x ^{5} - 765625 x ^{6} + 78125 i x ^{7}}

Viết lại

823543 - 4117715 i x - 8823675 x^{2} + 10504375 i x^{3} + 7503125 x^{4} - 3215625 i x^{5} - 765625 x^{6} + 78125 i x^{7}

ở dạng phức tiêu chuẩn:

(823543 - 8823675 x^{2} + 7503125 x^{4} - 765625 x^{6}) + (- 4117715 x + 10504375 x^{3} - 3215625 x^{5} + 78125 x^{7}) i

= \frac{1}{( 823543 - 8823675 x ^{2} + 7503125 x ^{4} - 765625 x ^{6} ) + ( - 4117715 x + 10504375 x ^{3} - 3215625 x ^{5} + 78125 x ^{7} ) i}

Nhân với liên hợp của

\frac{( 823543 - 8823675 x ^{2} + 7503125 x ^{4} - 765625 x ^{6} ) + ( 4117715 x - 10504375 x ^{3} + 3215625 x ^{5} - 78125 x ^{7} ) i}{( 823543 - 8823675 x ^{2} + 7503125 x ^{4} - 765625 x ^{6} ) + ( 4117715 x - 10504375 x ^{3} + 3215625 x ^{5} - 78125 x ^{7} ) i}

= \frac{1 \cdot ( ( 823543 - 8823675 x ^{2} + 7503125 x ^{4} - 765625 x ^{6} ) + ( 4117715 x - 10504375 x ^{3} + 3215625 x ^{5} - 78125 x ^{7} ) i )}{( ( 823543 - 8823675 x ^{2} + 7503125 x ^{4} - 765625 x ^{6} ) + ( - 4117715 x + 10504375 x ^{3} - 3215625 x ^{5} + 78125 x ^{7} ) i ) ( ( 823543 - 8823675 x ^{2} + 7503125 x ^{4} - 765625 x ^{6} ) + ( 4117715 x - 10504375 x ^{3} + 3215625 x ^{5} - 78125 x ^{7} ) i )}

Rút gọn

\frac{1 \cdot ( ( 823543 - 8823675 x ^{2} + 7503125 x ^{4} - 765625 x ^{6} ) + ( 4117715 x - 10504375 x ^{3} + 3215625 x ^{5} - 78125 x ^{7} ) i )}{( ( 823543 - 8823675 x ^{2} + 7503125 x ^{4} - 765625 x ^{6} ) + ( - 4117715 x + 10504375 x ^{3} - 3215625 x ^{5} + 78125 x ^{7} ) i ) ( ( 823543 - 8823675 x ^{2} + 7503125 x ^{4} - 765625 x ^{6} ) + ( 4117715 x - 10504375 x ^{3} + 3215625 x ^{5} - 78125 x ^{7} ) i )} : \frac{823543 - 8823675 x ^{2} + 7503125 x ^{4} - 765625 x ^{6} + i ( 4117715 x - 10504375 x ^{3} + 3215625 x ^{5} - 78125 x ^{7} )}{6103515625 x ^{14} + 83740234375 x ^{12} + 492392578125 x ^{10} + 1608482421875 x ^{8} + 3152625546875 x ^{6} + 3707487643125 x ^{4} + 2422225260175 x ^{2} + 678223072849}

= \frac{823543 - 8823675 x ^{2} + 7503125 x ^{4} - 765625 x ^{6} + i ( 4117715 x - 10504375 x ^{3} + 3215625 x ^{5} - 78125 x ^{7} )}{6103515625 x ^{14} + 83740234375 x ^{12} + 492392578125 x ^{10} + 1608482421875 x ^{8} + 3152625546875 x ^{6} + 3707487643125 x ^{4} + 2422225260175 x ^{2} + 678223072849}

Rewrite in standard complex form:

\frac{823543 - 8823675 x ^{2} + 7503125 x ^{4} - 765625 x ^{6}}{6103515625 x ^{14} + 83740234375 x ^{12} + 492392578125 x ^{10} + 1608482421875 x ^{8} + 3152625546875 x ^{6} + 3707487643125 x ^{4} + 2422225260175 x ^{2} + 678223072849} + \frac{4117715 x - 10504375 x ^{3} + 3215625 x ^{5} - 78125 x ^{7}}{6103515625 x ^{14} + 83740234375 x ^{12} + 492392578125 x ^{10} + 1608482421875 x ^{8} + 3152625546875 x ^{6} + 3707487643125 x ^{4} + 2422225260175 x ^{2} + 678223072849} i

= \frac{823543 - 8823675 x ^{2} + 7503125 x ^{4} - 765625 x ^{6}}{6103515625 x ^{14} + 83740234375 x ^{12} + 492392578125 x ^{10} + 1608482421875 x ^{8} + 3152625546875 x ^{6} + 3707487643125 x ^{4} + 2422225260175 x ^{2} + 678223072849} + \frac{4117715 x - 10504375 x ^{3} + 3215625 x ^{5} - 78125 x ^{7}}{6103515625 x ^{14} + 83740234375 x ^{12} + 492392578125 x ^{10} + 1608482421875 x ^{8} + 3152625546875 x ^{6} + 3707487643125 x ^{4} + 2422225260175 x ^{2} + 678223072849} i

Ví dụ phổ biến

khai triển (x+Δx)^2-2(x+Δx)+2

e x p an d (x + Δ x)^{2} - 2 (x + Δ x) + 2

khai triển-2/10 (1-2x+2)

e x p an d - \frac{2}{10} (1 - 2 x + 2)

khai triển (pgsin(θ)(-y^2+2L^2y))/(2Lm)

e x p an d \frac{p g sin ( θ ) ( - y ^{2} + 2 L ^{2} y )}{2 L m}

khai triển (x^2+2s+53)/((s^2+49)*(s+2))

e x p an d \frac{x ^{2} + 2 s + 53}{( s ^{2} + 49 ) \cdot ( s + 2 )}

rút gọn (sqrt(7-t)+2)^2

s im pl i f y (7 - t + 2)^{2}