i是虚数单位,复数1-i/i的立方等于多少
问题描述:
i是虚数单位,复数1-i/i的立方等于多少
答
(1-i/i)^3 = [ (1-i)*i / (i*i) ] ^3 = [ (i+1) / (-1) ] ^3
= - (1+i)^3 = - (1+i)^2*(1+i) = - (1-1+2i) * (1+i)
= - 2i *(1+i)
= -2i + 2
= 2-2i