We examine geometric constructions using Origami (paper folding), exploring the progression from classical ruler-and-compass methods to advanced multiple fold Origami techniques. We begin by reviewing ruler-and-compass constructions and their algebraic characterization through field extensions. We then introduce the seven Huzita-Justin axioms for single-fold Origami and demonstrate that axioms $O_1$ through $O_5$ produce exactly the ruler-and-compass constructible points, while axiom $O_6$ extends constructibility to solutions of cubic equations, including angle trisection. 

We investigate multiple fold axioms and present the result that $(n-2)$-fold Origami can construct real roots of degree $n$ polynomials using Lill's method. Our main contribution is proving that all quadratic equations with complex coefficients can be solved using two-fold Origami. We introduce Lill's Method for Complex Roots (LMCR), which finds polynomial roots through sequences of similar triangles in the complex plane, and provide an explicit construction method via the axiom AL13a7bb. This work demonstrates how Origami constructions transcend classical geometric limitations.