imaginary unit
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English[edit]
Etymology[edit]
So named because it takes on the role of unit for the imaginary part of a complex number.
Noun[edit]
imaginary unit (plural imaginary units)
 (number theory, complex analysis, quaternion theory) An imaginary number (in the case of complex numbers, usually denoted ) that is defined as a solution to the equation .
 2013, J. A. Sparenberg, Hydrodynamic Propulsion and Its Optimization, Springer, page 183,
 In Section 4.3 we introduced the imaginary unit with , in the complex space domain. In section 4.4 we introduced the complex unit with , in connection with the time dependency of the shape (4.4.16) of the swimming profile. These different imaginary units have no interaction, we leave unaltered the product .
 2014, Dennis G. Zill, Warren S. Wright, Advanced Engineering Mathematics, Ascend Learning (Jones & Bartlett Learning), 5th Edition, page 793,
 We now simply say that is the imaginary unit and define it by the property . Using the imaginary unit, we build a general complex number out of two real numbers.
 2021, Bruce Hunt, Locally Mixed Symmetric Spaces, Springer, page 123,
 Consider now in addition to the given , one of the totally imaginary units not contained in , and note that acts transitively on the set of totally imaginary units of a quaternion algebra; as we are assuming , we may in fact assume that with .
 2013, J. A. Sparenberg, Hydrodynamic Propulsion and Its Optimization, Springer, page 183,
Usage notes[edit]
 The imaginary unit of complex analysis is usually denoted . In some fields (for instance, electrical engineering), however, it is customarily denoted , to avoid confusion with the symbol for electric current.
 The complex numbers are generated by assuming a single imaginary unit, , and constructing the numbers , where and are real numbers.
 The quaternions (regardable as an extension of the complex numbers) are similarly generated by assuming three distinct imaginary units, , and constructing the numbers .
Translations[edit]
imaginary number
