The fundamental theorem of algebra states that a polynomial of degree with complex coefficients has values for which . The are called the roots of , with some of them possibly repeated. Thus the polynomial may be factored into linear terms as , where is some complex number. In the case of real coefficients, the roots are real or come in conjugate pairs.

This Demonstration considers polynomials of the form , with , , complex. The roots are shown as white dots at the centers of black patches.