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# Imaginary unit

The imaginary unit ${\displaystyle i={\sqrt {-1}}}$ is one of the four units of the domain of complex numbers. (The others are 1, –1 and ${\displaystyle -i}$). In electrical engineering applications, the symbol ${\displaystyle j}$ is generally used instead of ${\displaystyle i}$, which is then generally used as an iterator.[1] The imaginary unit is I in Wolfram Mathematica's InputForm and a blackboard bold lowercase I in StandardForm.
The square root of the imaginary unit is ${\displaystyle {\frac {1}{\sqrt {2}}}+{\frac {1}{\sqrt {2}}}i}$ (see A010503).
1. Paul J. Nahin, An Imaginary Tale: The Story of ${\displaystyle {\sqrt {-1}}}$. Princeton, New Jersey: Princeton University Press (1988): 125