若复数z=i+i2014，则z+10z的模等于6262．

Question

若复数z=i+i²⁰¹⁴，则

z

+(10)/(z)的模等于

6√(2)

6√(2)

．

Answer 1

z=i+i²⁰¹⁴=i+（i²）¹⁰⁰⁷=i+（-1）¹⁰⁰⁷=-1+i．
∴

.

z

+(10)/(z)=−1−i+(10)/(−1+i)＝−1−i+(10(−1−i))/((−1+i)(−1−i))
=−1−i+(−10−10i)/(2)＝−6−6i．
∴|

.

z

+(10)/(z)|＝|−6−6i|＝6√(2)．
故答案为：6√(2)．