imaginary unit

Definitions

An imaginary number (in the case of complex numbers, usually denoted i) that is defined as a solution to the equation x²=-1.

Equivalents

Examples

“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.”

“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.”

“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'.”

CEFR level