A complex substrate for a display apparatus, the complex substrate includes a lower base substrate including convex and concave patterns, the convex and concave patterns being integral with an upper side of the lower base substrate, a planarizing layer on the lower base substrate, the planarizing layer being integral with the convex and concave patterns, and the planarizing layer having different refractivity from the lower base substrate, and a wire grid pattern on the planarizing layer, the wire grid pattern including a plurality of nano wire metal patterns, each of the nano wire metal patterns having a width of no more than a micrometer.