complex numbers

Given that z=-2+i , express z+1/sqrtz in the form of a+bi

i try squarring z :

\sqrt(-2+i)=a+bi
-2+i=a^2-b^2+2abi

By comparing , i got \sqrt(-2+i)=0.343a+1.458i and my answer looks weird to me . I am also not sure how to continue from here :

-2+i+1/(0.343a+1.458i )

thanks for helping .