kompleksverdig

Kompleksverdig is a Norwegian term used in mathematics and related disciplines to describe quantities that assume complex values. It is the direct translation of the English term complex-valued. In practice, a complex-valued object can be represented as z = a + ib, where a and b are real numbers and i is the imaginary unit.

The term is common in textbooks and technical writings when distinguishing between real-valued and complex-valued functions, signals, or random variables. Examples include complex-valued functions f: C -> C, complex-valued time signals x(t) = x_r(t) + i x_i(t) in signal processing, and complex-valued random variables in probability theory.

In use, complex-valued quantities are manipulated with standard algebraic operations extended to the complex plane, including addition, multiplication, complex conjugation, and magnitude |z| = sqrt(a^2 + b^2). When analyzing such quantities, it is common to separate them into real and imaginary parts, or into magnitude and phase representation z = r e^{iθ}.

Applications are widespread: in electrical engineering for phasor representation and Fourier analysis; in quantum mechanics for wavefunctions that have complex amplitudes; in control theory and communications for filters and transfer functions with complex-valued frequencies.

Notes: The term appears mainly in Norwegian-language literature. In English-language contexts, you would typically encounter complex-valued or complex-valued function to convey the same meaning.