The nth root of a real or complex number

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The nth root of a real number

The nth root of a real number b is the number x defined by xⁿ = b.
This is a polynomial equation of degree n.
According to the Fundamental Theorem of Algebra, this equation has n solutions.
This means that b has n nth roots.

It is clear from the foregoing that the nth root of a real or complex number can be obtained easily multiplying the absolute value of the number with the n nth roots of 1. This animation gives the picture using the "Argand" diagram of these roots of "unity" for small values of n.

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