已知w是1的七次方根
已知w是1的七次方根。求w/(1+w^2)+w^2/(1+w^4)+w^3/(1+w^6)的值已知w是1的七次方根。求w/(1+w^2)+w^2/(1+w^4)+w^3/(1+w^6)的值。请详解
题:已知w是1的七次方根。求w/(1+w^2)+w^2/(1+w^4)+w^3/(1+w^6)的值。请详解 解: 已知w是1的七次方根,则有两种可能: 其一,w=1,则w/(1+w^2)+w^2/(1+w^4)+w^3/(1+w^6)=3/2. 其二,w为非1的复根,则满足下列条件 1+w+w^2+w^3+w^4+w^5+w^6=0,w^7=1. 根据此条件进行简化,则有 w/(1+w^2)+w^2/(1+w^4)+w^3/(1+w^6) =(w(1+w^4)(1+w^6)+w^2(1+w^2)(1+w^6)+w^3(1+w^2)(1+w^4))/((1+w^2)(1+w^4)(1+w^6)) =2(1+w+w^2+w^3+w^4+w^5)/(1+w+w^2+w^3+w^4+w^5+2w^6) = -2w^6/w^6 = -2. 解毕.
已知w是1的七次方根,说明w=1 w/(1+w^2)+w^2/(1+w^4)+w^3/(1+w^6)=3/2
答:z是1的一个7次方根,并且z<>1.可以设z=cos(2pi/7)+isin(2pi/7) 则z^2=cos(4pi/7)+isin(4pi/7) z^4=co...详情>>
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