早教吧作业答案频道 -->数学-->
设Z=cos2π/3-isin2π/3,求Z^2,Z^3及Z^2+Z+1的值,
题目详情
设Z=cos2π/3-isin2π/3,求Z^2,Z^3及Z^2+Z+1的值,
▼优质解答
答案和解析
少了个i
Z=cos2π/3-isin2π/3
所以Z^2=cos(2×2π/3)-isin(2×2π/3)
=cos4π/3-isin4π/3
=-(1+i√3)/2
Z^3=cos(3×2π/3)-isin(3×2π/3)
=cos2π-isin2π
=1
Z^2+Z+1
=-(1+i√3)/2+(-1-i√3)/2+1
=-i√3
Z=cos2π/3-isin2π/3
所以Z^2=cos(2×2π/3)-isin(2×2π/3)
=cos4π/3-isin4π/3
=-(1+i√3)/2
Z^3=cos(3×2π/3)-isin(3×2π/3)
=cos2π-isin2π
=1
Z^2+Z+1
=-(1+i√3)/2+(-1-i√3)/2+1
=-i√3
看了设Z=cos2π/3-isin...的网友还看了以下:
求拉格朗日乘数求极值从二元单条件限制推广到多元多条件限制的证明如求F=f(X,Y,Z,T)在g(X 2020-04-25 …
已知集合A={z||z|≤1},(1)求集合A中复数z=x+yi所对应的复平面内动点坐标(x,y) 2020-06-14 …
下列命题(为虚数单位)中正确的是①a,b∈R,若a>b,则a+i>b+i;②当z是非零实数时,|z 2020-07-30 …
已知m∈R,复数z=(2+i)m2-3(1+i)m-2(1-i),(1)写出复数z的代数形式;(2 2020-08-01 …
已知i是虚数单位,且复数z满足(z-3)(2-i)=5.(Ⅰ)求z及|z-2+3i|;(Ⅱ)若z• 2020-08-01 …
已知m∈R,复数z=(2+i)m2-m(1-i)-(1+2i)(其中i为虚数单位).(1)当实数m 2020-08-01 …
(1)已知i是虚数单位,若复数z满足z(1+i)=2i,计算|z|;(2)若复数(m2-5m+6) 2020-08-01 …
设复数z=a+i(i是虚数单位,a∈R,a>0),且|z|=10.(Ⅰ)求复数z;(Ⅱ)在复平面内 2020-08-02 …
设复数z满足4z+2z=3√3+i,ω=sinθ-icosθ(θ∈R)求z的值及|z-ω|的取值范 2020-08-02 …
计算:(1)i(2-i)(3+i)(2)设复数z满足z+|z|=2+i,求z的值(3)(2+2i)2 2020-11-01 …