We investigate the complementarity relation among the $l_{1}$ norm of imaginarity, linear entropy and the Brukner-Zeilinger invariant information in the presence of conjugate

 symmetry.By using an equality derived from the complementarity relation, we define a quantity named index of imaginarity distribution with respect to the imaginarity,

 linear entropy and invariant information in finite dimensional quantum systems. We show that the index of imaginarity distribution is nonnegative and upper bounded by the square 

of the $l_{1}$ norm of imaginarity, and serves as an invaluable tool in characterizing effectively the imaginarity distribution.

Detailed examples are presented to illustrate our theoretical analysis.