COMPLEX

Complex is an adjective and noun with several related meanings. As an adjective, it describes something consisting of many interconnected parts, intricate or not easily understood. It is used for systems, problems, ideas, or structures. The word derives from Latin complexus, from complere "to enfold" or "to embrace". As a noun, it can refer to a group of buildings (a shopping complex), a set of related ideas or emotions (a psychological complex), or a discrete mathematical object (a complex number).

A complex number is a number of the form a + bi, where a and b are real numbers and i is the imaginary unit with i^2 = -1. The set of all complex numbers is denoted C. They can be added and multiplied, with conjugate a - bi, modulus sqrt(a^2 + b^2), and argument arctan(b/a). Geometrically they can be plotted on the complex plane; operations correspond to rotations and scalings. The Fundamental Theorem of Algebra states that every non-constant polynomial over C has a root in C.

In psychology, a complex is a cluster of related ideas, memories, and feelings organized around a theme, often with emotional charge. Notable examples include the Oedipus complex (Freud) and the inferiority complex (Adler). In ordinary language, "complex" also denotes a set of interrelated attitudes or traits.

As a noun, complex can refer to a group of buildings (sports complex, military complex). In linguistics, a complex sentence contains an independent clause and one or more dependent clauses. The phrase military–industrial complex denotes the relationship between a nation's military, industry, and politics.