早教吧作业答案频道 -->数学-->
w=-1/2+根号3/2i,则w4+w2+1=
题目详情
w=-1/2+根号3/2i,则w4+w2+1=
▼优质解答
答案和解析
w=-1/2+根号3/2i=cos(2π/3) +sin(2π/3)*i
则：w^4+w²+1
=cos(8π/3) +sin(8π/3)*i +cos(4π/3) +sin(4π/3)*i +1
=cos(2π/3) +sin(2π/3)*i -cos(π/3) -sin(π/3)*i +1
=-cos(π/3) +sin(π/3)*i -cos(π/3) -sin(π/3)*i +1
=-2cos(π/3)+1
=0
则：w^4+w²+1
=cos(8π/3) +sin(8π/3)*i +cos(4π/3) +sin(4π/3)*i +1
=cos(2π/3) +sin(2π/3)*i -cos(π/3) -sin(π/3)*i +1
=-cos(π/3) +sin(π/3)*i -cos(π/3) -sin(π/3)*i +1
=-2cos(π/3)+1
=0
看了w=-1/2+根号3/2i,则...的网友还看了以下：
（2011•普陀区三模）已知复数满足w-4=（3-2w）i（i为虚数单位），z＝5w+|w−2|， 2020-05-13 …
甲乙两人受到的重力之比G甲：G乙=4:3,甲从一楼到二楼,乙从二楼到三楼俩人克服重力所做的功之比W 2020-05-19 …
设w=-1/2+根号3/2i,求(1+w)(1+w^2)(1+w^4)(1+w^8)的值 2020-06-12 …
已知复数w满足w-4=（3-2w）i（i为虚单位）,1求复数w2求一个以复数为w根的实系数一元二次 2020-06-12 …
复变函数解方程(1+w)^4=(1-w)^4 2020-06-12 …
limx→∞(x^4+3x-1)/(3x^4+4x^2+1)对分式(x^4+3x-1)/(3x^4 2020-06-27 …
1×2=1/3(1×2×3-0×1×2)2×3=1/3(2×3×4-1×2×3)3×4=1/3(3 2020-07-19 …
观察下列各式:1×2=1/3(1×2×3-0×1×2)2×3=1/3(2×3×4-1×2×3)3× 2020-07-31 …
已知复数w满足w-4=（3-2w）i（i为虚数单位），z=5w+|w-2|，求一个以z为根的实系数 2020-08-02 …
观察下列等式:1/1*2=1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4.在线等 2020-12-05 …