Introductry Mathematics by Prof. Soham Kulkarni

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Similar to how solving real quadratic equations can result in new complex numbers, solving equations with complex coefficients can result in even more diverse new numbers.
Complex numbers alone, according to Jean D'Alembert (1717–1783), would be sufficient.
This is supported by Gauss' assertion that "every polynomial equation has a complex root" in the Fundamental Theorem of Algebra.
A definition of complex numbers as ordered pairs of real numbers subject to specific explicit manipulation constraints was published in 1837, over three centuries after Cardan first used imaginary numbers.

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