Imaginary unit

In mathematics, the imaginary unit i (sometimes also represented by j, but in this article i will be used exclusively) allows the real number system mathbb{R} to be extended to the complex number system mathbb{C}. Its precise definition is dependent upon the particular method of extension.

Related Topics:
Mathematics - Real number - Complex number

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The primary motivation for this extension is the fact that not every polynomial equation f(x) = 0 has a solution in the real numbers. In particular, the equation x2 + 1 = 0 has no real solution. However, if we allow complex numbers as solutions, then this equation, and indeed every polynomial equation f(x) = 0 does have a solution. (See algebraic closure and fundamental theorem of algebra.)

Related Topics:
Polynomial equation - Solution - Algebraic closure - Fundamental theorem of algebra

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