针对你的题目,将复数写成指数形式算是较为简便的：
exp(iπ/4)=cos(π/4)+isin(π/4)=(1+i)/√2
exp(-iπ/6)=(1-i√3)/2
所以原式=[(2√2)^4]exp(iπ)/{(2^5)(exp(-i5π/6)}
=-2/exp(-i5π/6)
=-2exp(5iπ/6)
=-1+√3