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A complex number is an expression of the form a + bi, where a and b are real numbers, and i is an abstract symbol, the so-called imaginary unit, whose meaning will be explained further below. For example, 2 + 3i is a complex number. [3]
A complex system is a system composed of many components which may interact with each other. [1] Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an ecosystem, a living cell, and, ultimately, for ...
Complex commonly refers to: Complexity , the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe Complex system , a system composed of many components which may interact with each other
An illustration of the complex plane. The imaginary numbers are on the vertical coordinate axis. Although the Greek mathematician and engineer Heron of Alexandria is noted as the first to present a calculation involving the square root of a negative number, [6] [7] it was Rafael Bombelli who first set down the rules for multiplication of complex numbers in 1572.
The study of these complex linkages at various scales is the main goal of complex systems theory. The intuitive criterion of complexity can be formulated as follows: a system would be more complex if more parts could be distinguished, and if more connections between them existed.
The above properties actually define a real structure on the complex vector space . [2] One example of this notion is the conjugate transpose operation of complex matrices defined above. However, on generic complex vector spaces, there is no canonical notion of complex conjugation.
An example of a complex would be as follows: if a person had a leg amputated as a child, this would influence the person's life in profound ways, even upon overcoming the physical handicap. The person may have many thoughts, emotions, memories, feelings of inferiority, triumphs, bitterness, and determinations centering on that one aspect of life.
An example of a non-homogeneous complex is a triangle with a line segment attached to one of its vertices. Pure simplicial complexes can be thought of as triangulations and provide a definition of polytopes .