z=a+bi
|2(a+bi)-i|=2
|2a+(2b-1)i|=2
2a*2a+(2b-1)*(2b-1)=4
a*a=3/4-b*b+b
|z+2i|=|a+bi+2i|=[a*a+(b+2)*(b+2)]的平方根
a*a+(b+2)*(b+2)=3/4-b*b+b+b*b+4b+4=19/4+5b
因为2a*2a+(2b-1)*(2b-1)=4
(2b-1)*(2b-1)=4-4a*a<=4
-1/2<=b<=3/2
19/4+5b>=9/4
[a*a+(b+2)*(b+2)]的平方根>=3/2
|z＋2i|的最小值是3/2