imaginary unit
nounEtymology So named because it takes on the role of unit for the imaginary part of a complex number.
1
Complex analysis, Mathematics, Number theory, Sciences An imaginary number (in the case of complex numbers, usually denoted i) that is defined as a solution to the equation x²=-1.
Quaternion theory
- In Section 4.3 we introduced the imaginary unit i with (i)²#61;-1, in the complex space domain. In section 4.4 we introduced the complex unit j with (j)²#61;-1, 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 ij.2013, J. A. Sparenberg, Hydrodynamic Propulsion and Its Optimization, Springer, page 183:
- 2014, Dennis G. Zill, Warren S. Wright, Advanced Engineering Mathematics, Ascend Learning (Jones & Bartlett Learning), 5th Edition, page 793, We now simply say that i is the imaginary unit and define it by the property i²=-1. Using the imaginary unit, we build a general complex number out of two real numbers.
1 more example
- Consider now in addition to the given #92;H#92;subset#92;mathbb#123;O#125;, one of the totally imaginary units not contained in #92;H, and note that #123;SU#125;(2) acts transitively on the set of totally imaginary units of a quaternion algebra; as we are assuming #92;alpha#92;notin#92;H, we may in fact assume that #92;mathbb#123;O#125;#61;#92;H#92;oplus#92;H' with #92;alpha#92;in#92;H'.2021, Bruce Hunt, Locally Mixed Symmetric Spaces, Springer, page 123: