如题所述
i^2017=i•i^2016
=i•(i²)^1008
=i•(-1)^1008=i
∴z=i/(1+i)=i(1-i)/(1+i)(1-i)
=(i-i²)/(1-i²)=(1+i)/2
∴|z|=√(1/2)² + (1/2)²
=√1/4 + 1/4=√2/4
=√2/2
=i•(i²)^1008
=i•(-1)^1008=i
∴z=i/(1+i)=i(1-i)/(1+i)(1-i)
=(i-i²)/(1-i²)=(1+i)/2
∴|z|=√(1/2)² + (1/2)²
=√1/4 + 1/4=√2/4
=√2/2
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