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  2. Imaginary unit - Wikipedia

    en.wikipedia.org/wiki/Imaginary_unit

    The imaginary unit i in the complex plane: Real numbers are conventionally drawn on the horizontal axis, and imaginary numbers on the vertical axis.. The imaginary unit or unit imaginary number (i) is a mathematical constant that is a solution to the quadratic equation x 2 + 1 = 0.

  3. Imaginary number - Wikipedia

    en.wikipedia.org/wiki/Imaginary_number

    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.

  4. Complex number - Wikipedia

    en.wikipedia.org/wiki/Complex_number

    In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation =; every complex number can be expressed in the form +, where a and b are real numbers.

  5. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    In mathematics, Euler's identity [note 1] (also known as Euler's equation) is the equality + = where . is Euler's number, the base of natural logarithms, is the imaginary unit, which by definition satisfies =, and

  6. Identity matrix - Wikipedia

    en.wikipedia.org/wiki/Identity_matrix

    Less frequently, some mathematics books use or to represent the identity matrix, standing for "unit matrix" [2] and the German word Einheitsmatrix respectively. [ 8 ] In terms of a notation that is sometimes used to concisely describe diagonal matrices , the identity matrix can be written as I n = diag ⁡ ( 1 , 1 , … , 1 ) . {\displaystyle I ...

  7. List of large cardinal properties - Wikipedia

    en.wikipedia.org/wiki/List_of_large_cardinal...

    Wholeness axiom, rank-into-rank (Axioms I3, I2, I1, and I0) The following even stronger large cardinal properties are not consistent with the axiom of choice, but their existence has not yet been refuted in ZF alone (that is, without use of the axiom of choice ).

  8. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]

  9. e (mathematical constant) - Wikipedia

    en.wikipedia.org/wiki/E_(mathematical_constant)

    The number e is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function.It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted .