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An imaginary number is the product of a real number and the imaginary unit i, [note 1] which is defined by its property i 2 = −1. [1] [2] The square of an imaginary number bi is −b 2. For example, 5i is an imaginary number, and its square is −25. The number zero is considered to be both real and imaginary. [3]
A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.
The imaginary unit or unit imaginary number (i) is a mathematical constant that is a solution to the quadratic equation x 2 + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of i in a complex ...
By "unreal" number you mean a number which can be replaced by "pure numbers" only (probably this is the article you're looking for), whereas by "real" number you mean a number that can be replaced by an apple or by a meter and likewise. So yes, the 2 in the term 2^3 is really real - because you can replace it by a meter (thus getting the volume ...
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. [a] Every real number can be almost uniquely represented by an infinite decimal expansion. [b] [1]
A surcomplex number is a number of the form a + bi, where a and b are surreal numbers and i is the square root of −1. [10] [11] ...
A computable number [is] one for which there is a Turing machine which, given n on its initial tape, terminates with the nth digit of that number [encoded on its tape]. The key notions in the definition are (1) that some n is specified at the start, (2) for any n the computation only takes a finite number of steps, after which the machine ...