An infinite two-dimensional space representing the set of complex numbers, especially one in which Cartesian coordinates represent the real and imaginary parts of the complex numbers.
- Cauchy developed his theory fitfully from the 1810s to the 1840s, and this version of his theorem is the last one, with the complex plane available as the site for C.
- Over much of the complex plane the function turns out to be wildly oscillatory, crossing from positive to negative values infinitely often.
- As the Fundamental Theorem of Algebra clearly indicates, the complex plane rather than the real line is the proper place for the study of polynomials.
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