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  2. Cube root - Wikipedia

    en.wikipedia.org/wiki/Cube_root

    In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other cube roots of ...

  3. Root of unity - Wikipedia

    en.wikipedia.org/wiki/Root_of_unity

    For n = 8, for any root of unity z + z equals to either 0, ±2, or ± √ 2 (D = 2). For n = 12, for any root of unity, z + z equals to either 0, ±1, ±2 or ± √ 3 (D = 3). See also. Argand system; Circle group, the unit complex numbers; Cyclotomic field; Group scheme of roots of unity; Dirichlet character; Ramanujan's sum; Witt vector ...

  4. Cubic equation - Wikipedia

    en.wikipedia.org/wiki/Cubic_equation

    The other roots of the equation are obtained either by changing of cube root or, equivalently, by multiplying the cube root by a primitive cube root of unity, that is . This formula for the roots is always correct except when p = q = 0 , with the proviso that if p = 0 , the square root is chosen so that C ≠ 0 .

  5. Cube (algebra) - Wikipedia

    en.wikipedia.org/wiki/Cube_(algebra)

    The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x + 1)3 . The cube is also the number multiplied by its square : n3 = n × n2 = n × n × n. The cube function is the function x ↦ x3 (often denoted y = x3) that maps a number to its cube. It is an odd function, as.

  6. Imaginary unit - Wikipedia

    en.wikipedia.org/wiki/Imaginary_unit

    The imaginary unit or unit imaginary number ( i) is a solution to the quadratic equation x2 + 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 number is 2 + 3i.

  7. nth root - Wikipedia

    en.wikipedia.org/wiki/Nth_root

    For n equal to 2 this is called the principal square root and the n is omitted. ... Answer is 12.34 Find the cube root of 4192 truncated to the nearest thousandth.

  8. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.

  9. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    Quadratic equation. In mathematics, a quadratic equation (from Latin quadratus ' square ') is an equation that can be rearranged in standard form as [1] where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.

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