komplekser

Komplekser is a term used in several languages to refer to concepts that are composed of interconnected parts. In everyday usage it most often denotes psychological patterns, while in mathematics it can refer to complex numbers. The common etymology traces to the Latin complexus, meaning “woven together.”

In psychology, a complex is a cluster of related ideas, memories, and emotions that influence perception and behavior, often operating at an unconscious level. Jungian psychology popularized the term to describe enduring patterns tied to particular themes, such as the Inferiority Complex or the Oedipus Complex. Complexes can arise from early experiences and may interact with the ego, shaping attitudes and reactions.

In mathematics, complex numbers extend the real numbers by including an imaginary unit i, with i^2 = -1. A typical complex number is written z = a + bi, where a is the real part and b is the imaginary part. The set of all complex numbers, denoted C, can be added and multiplied, and each nonzero complex number has a unique multiplicative inverse. Complex numbers can be represented graphically on the complex plane, with modulus r = sqrt(a^2 + b^2) and argument theta. They can be expressed in polar form r(cos theta + i sin theta) or compactly as re^(i theta). Operations such as conjugation, addition, multiplication, and division are standard; they enable techniques in signal processing, quantum physics, and engineering among others.

Etymology and usage vary by language, but the core idea of komplekser as interconnected parts appears across disciplines, from inner psychological patterns to the algebraic structure of complex numbers.