Definition:Square Root/Complex Number/Definition 3
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Definition
Let $z \in \C$ be a complex number.
The square root of $z$ is the $2$-valued multifunction:
- $z^{1/2} = \set {\sqrt {\cmod z} \, e^{\paren {i / 2} \map \arg z} }$
where:
- $\sqrt {\cmod z}$ denotes the positive square root of the complex modulus of $z$
- $\map \arg z$ denotes the argument of $z$ considered as a multifunction.
Also see
Sources
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions ... (previous) ... (next): $3$: Elementary Analytic Methods: $3.7$ Complex Numbers and Functions: Roots: $3.7.26$