A perplex number (also known as a split-complex number or a hyperbolic number or a Lorentz number or myriad other such synonyms varying from author to author) is an expression of the form , where and are real numbers and (but ). The set of perplex numbers (in fact a topological vector space and commutative algebra over the real numbers) may be denoted or .
notice that the absolute value of a perplex number is a complex number, with
But this absolute value is degenerate, in that need not imply that .
Some concepts in analysis can be extended from to , but not as many as work for the complex numbers. Even algebraically, the perplex numbers are not as nice as the real or complex numbers, as they do not form a field.
Revised on November 20, 2011 10:42:51
by Sridhar Ramesh