计算Z＝（-1+i/1+根号3i）的6次方

题目

计算Z＝（-1+i/1+根号3i）的6次方

答案

Z＝（-1+i/1+根号3i）的6次方
=[(-1+i)^2/(1+根号3i)^2]^3
=[(-2i)/(2+2根号3i)]^3
=[-i/(1+√3i)]^3
=i/[(1+√3i)^2*(1+√3i)]
=i/[(-2+2√3i)(1+√3i)]
=i/8