imaginary unit

Etymology
So named because it takes on the role of unit for the imaginary part of a complex number.

Noun

 * 1)  An imaginary number (in the case of complex numbers, usually denoted $$i$$) that is defined as a solution to the equation $$x^2 = -1$$.
 * 2) * 2014, Dennis G. Zill, Warren S. Wright, Advanced Engineering Mathematics, Ascend Learning, 5th Edition, page 793,
 * We now simply say that $$i$$ is the imaginary unit and define it by the property $$i^2 = -1$$. Using the imaginary unit, we build a general complex number out of two real numbers.
 * We now simply say that $$i$$ is the imaginary unit and define it by the property $$i^2 = -1$$. Using the imaginary unit, we build a general complex number out of two real numbers.

Usage notes

 * The imaginary unit of complex analysis is usually denoted $$i$$. In some fields (for instance, electrical engineering), however, it is customarily denoted $$j$$, to avoid confusion with the symbol for electric current.
 * The complex numbers are generated by assuming a single imaginary unit, $$i$$, and constructing the numbers $$a+bi$$, where $$a$$ and $$b$$ are real numbers.
 * The quaternions (regardable as an extension of the complex numbers) are similarly generated by assuming three distinct imaginary units, $$i, j, k$$, and constructing the numbers $$a+bi+cj+dk$$.

Translations

 * Finnish:
 * French:
 * German:
 * Hindi: अधिकल्पित एकक
 * Italian:
 * Japanese:
 * Korean: 허수단위
 * Latin: unitas imaginaria
 * Russian:
 * Thai: หน่วยจินตภาพ