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As early as the sixteenth century, mathematicians were using numbers with i included—the so-called complex numbers—to solve cubic and quartic polynomials.

It’s a model of a surface called the Klein quartic.

A curve of the third order is called a cubic; one of the fourth order a quartic; and so on.

The singular surface of the general quadratic complex is the famous quartic, with sixteen nodes and sixteen singular tangent planes, first discovered by E.E.

But when the quartic is numerical the same thing happens as in the cubic, and the algebraical solution does not in every case give the numerical one.