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2. Conjugate (square roots) - Wikipedia

   en.wikipedia.org/wiki/Conjugate_(square_roots)

   In mathematics, the conjugate of an expression of the form + is , provided that does not appear in a and b.One says also that the two expressions are conjugate. In particular, the two solutions of a quadratic equation are conjugate, as per the in the quadratic formula =.

3. Complex conjugate - Wikipedia

   en.wikipedia.org/wiki/Complex_conjugate

   Geometric representation (Argand diagram) of and its conjugate ¯ in the complex plane.The complex conjugate is found by reflecting across the real axis.. In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.

4. Complex conjugate root theorem - Wikipedia

   en.wikipedia.org/wiki/Complex_conjugate_root_theorem

   In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P. [1]

5. Split-complex number - Wikipedia

   en.wikipedia.org/wiki/Split-complex_number

   Addition and multiplication of split-complex numbers are then given by matrix addition and multiplication. The squared modulus of z is given by the determinant of the corresponding matrix. In fact there are many representations of the split-complex plane in the four-dimensional ring of 2x2 real matrices.

6. Complex conjugate of a vector space - Wikipedia

   en.wikipedia.org/wiki/Complex_conjugate_of_a...

   In other words, the scalar multiplication of ¯ satisfies = ¯ where is the scalar multiplication of ¯ and is the scalar multiplication of . The letter v {\displaystyle v} stands for a vector in V , {\displaystyle V,} α {\displaystyle \alpha } is a complex number, and α ¯ {\displaystyle {\overline {\alpha }}} denotes the complex conjugate ...

7. Conjugate variables - Wikipedia

   en.wikipedia.org/wiki/Conjugate_variables

   Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, [1] [2] or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation—in physics called the Heisenberg uncertainty principle —between them.