Complex numbers arose from the desire to solve algebraic equations—that is, equations obtained by setting a polynomial equal to zero—and quadratic equations in particular.
The number i, a symbol
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The stumbling block that took centuries to overcome was solving the equation X2 = -1, elementary though it is. It led to the creation of i, a number called "imaginary" because it could not be accommodated within the "real" numbers that had until then formed the universally accepted framework for algebraic computation.
The shock can be compared to the revolution that shook the Pythagorean school when irrational numbers were discovered.
The number i symbolizes a new approach to mathematics. To begin with, it makes it possible to solve all quadratic equations with real coefficients, yielding two roots even when the discriminant is negative (see box).
