((-1+√3i)^3/(1+i)^6)-((-2+i)/(1+2i))过程怎么写

题目

((-1+√3i)^3/(1+i)^6)-((-2+i)/(1+2i))过程怎么写

答案

(1+i)^6 = (1-1+2i)^3=(2i)^3 = 8*i*i*i=-8i
(-1+√3i)^3 = (-1+√3i)*(1-3-2√3i) = (-1+√3i)*(-2-2√3i) = -2(-1+√3i)*(1+√3i)=-2(-3-1)=8
因此 (-1+√3i)^3/(1+i)^6) = 8/(-8i) = -1/i = i
(-2+i)/(1+2i) = (-2+i)(1-2i) / [(1+2i)(1-2i)] = (-2+i+4i+2) / (1+4) = i
因此
((-1+√3i)^3/(1+i)^6) - ((-2+i)/(1+2i))
= i - i
= 0