imaginär

Imaginär is a German adjective meaning imaginary. In everyday language it describes things that exist only in the mind, in fiction, or in concepts not grounded in physical reality. In scientific and mathematical usage, imaginär refers to the concept of imaginary numbers. The term derives from Latin imaginarius, via French imaginaire, and entered German through scholarly Latin and French mathematical writings.

In mathematics, an imaginary number is a multiple of the imaginary unit i, where i^2 = -1. Imaginary numbers are combined with real numbers to form complex numbers of the form a + bi, with a and b real. The set of complex numbers is represented as the complex plane, where the real part corresponds to the horizontal axis and the imaginary part to the vertical axis. The magnitude and argument of a complex number describe its size and direction in this plane. In many engineering fields, the symbol j is used instead of i to denote the imaginary unit, to avoid confusion with electric current denoted by i.

Beyond mathematics, imaginär appears in philosophy, literature, and cultural discourse to discuss entities or scenarios that are conceivable or fictional rather than physically real. The distinction between real (reell) and imaginary (imaginär) is a common theme when evaluating theories, hypotheses, or stories.

Examples include the imaginary unit i in complex numbers such as 3 + 4i, and the phrase “imaginäre Welten” describing fictional realms. The term thus spans precise technical use and broader metaphorical meaning.