[√2/(1+i)]²
=2/(1+i)²
=2/(2i)
=1/i
=-i
则:[√2/(1+i)]^4=1
则原式=1^5=1
[√2/(1+i)]^20=【[√2/(1+i)]^4】^5=1^5=1
=【[√2/(1+i)]^2】^10=(2/2i)^10=i^10=(i^2)^5=(-1)^5=-1。。。。。。看了前面那个算了下怎么是这个
是我算错了,答案应该是-1正确解答如下:[√2/(1+i)]²=2/(1+i)²=2/(2i)=1/i=-i则:[√2/(1+i)]^4=(-i)²=-1则原式=(-1)^5=-1