Definition:Complex Root
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Definition
Let $z \in \C$ be a complex number such that $z \ne 0$.
Let $n \in \Z_{>0}$ be a (strictly) positive integer.
Let $w \in \C$ such that:
- $w^n = z$
Then $w$ is a (complex) $n$th root of $z$, and we can write:
- $w = z^{1 / n}$
Also see
- Roots of Complex Number, where it is demonstrated what the complex $n$th roots actually are in terms of $z$ and $n$.
Sources
- 1957: E.G. Phillips: Functions of a Complex Variable (8th ed.) ... (previous) ... (next): Chapter $\text I$: Functions of a Complex Variable: $\S 3$. Geometric Representation of Complex Numbers
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 3$. Roots of Unity: $(3.8)$
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Roots of Complex Number