复数i/1+2i的实部是?正负2/5,还是正负1/5

问题描述:

复数i/1+2i的实部是?正负2/5,还是正负1/5

由i/(i+2i)
=(1-2i)i/(1+2i)(1-2i)
=(1-2i)i/(1-4i²)
∵i²=-1,
∴(1-2i)i/(1-4i²)
=(1-2i)i/5
=(i+2)/5
=2/5+i/5
实部为2/5.