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  2. Imaginary unit - Wikipedia

    en.wikipedia.org/wiki/Imaginary_unit

    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 .

  3. Complex number - Wikipedia

    en.wikipedia.org/wiki/Complex_number

    For the complex number +, a is called the real part, and b is called the imaginary part. The set of complex numbers is denoted by either of the symbols C {\displaystyle \mathbb {C} } or C . Despite the historical nomenclature, "imaginary" complex numbers have a mathematical existence as firm as that of the real numbers, and they are fundamental ...

  4. Imaginary number - Wikipedia

    en.wikipedia.org/wiki/Imaginary_number

    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]

  5. Cubic equation - Wikipedia

    en.wikipedia.org/wiki/Cubic_equation

    The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). All of the roots of the cubic equation can be found by ...

  6. Extraneous and missing solutions - Wikipedia

    en.wikipedia.org/wiki/Extraneous_and_missing...

    A missing solution is a valid one which is lost during the solution process. Both situations frequently result from performing operations that are not invertible for some or all values of the variables involved, which prevents the chain of logical implications from being bidirectional.

  7. Today's Wordle Hint, Answer for #1343 on Friday, February 21 ...

    www.aol.com/todays-wordle-hint-answer-1343...

    Hints and the solution for today's Wordle on Friday, February 21.

  8. Common integrals in quantum field theory - Wikipedia

    en.wikipedia.org/wiki/Common_integrals_in...

    The one-dimensional integrals can be generalized to multiple dimensions. [2] ⁡ (+) = ⁡ ()Here A is a real positive definite symmetric matrix.. This integral is performed by diagonalization of A with an orthogonal transformation = = where D is a diagonal matrix and O is an orthogonal matrix.

  9. Closed-form expression - Wikipedia

    en.wikipedia.org/wiki/Closed-form_expression

    The quadratic formula =. is a closed form of the solutions to the general quadratic equation + + =. More generally, in the context of polynomial equations, a closed form of a solution is a solution in radicals; that is, a closed-form expression for which the allowed functions are only n th-roots and field operations (+,,, /).

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