复数计算(√3i-1)^10+(-√3i-1)^10

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/24 11:28:33
复数计算(√3i-1)^10+(-√3i-1)^10
x){ /-|n=:fgjhk"lQ/!ՂOF4t * j$50%mFRڙřyf,J py1F&c P1(Ԇ+0DU`Un  0A5A2% B0!] =<;P,IJ

复数计算(√3i-1)^10+(-√3i-1)^10
复数计算
(√3i-1)^10+(-√3i-1)^10

复数计算(√3i-1)^10+(-√3i-1)^10
原式=[2^10(-1/2+√3i/2)^10]+2^10[(1/2+√3i/2)^10]
=2^10[cos(2π/3)+isin(2π/3)]^10+2^10[cos(π/3)+isin(π/3)]^10
=1024[cos(20π/3)+isin(20π/3)]+1024[cos(10π/3)+isin(10π/3)]
=1024[cos(2π/3)+isin(2π/3)+1024[cos(4π/3)+isin(4π/3)]
1024(-1/2+√3i/2)+1024(-1/2-√3i/2)
=-1024.