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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. That is, if a {\displaystyle a} and b {\displaystyle b} are real numbers, then the complex conjugate of a + b i {\displaystyle a+bi} is a − b i . {\displaystyle a-bi.}
On the other hand, if a chemical is a weak acid its conjugate base will not necessarily be strong. Consider that ethanoate, the conjugate base of ethanoic acid, has a base splitting constant (Kb) of about 5.6 × 10 −10, making it a weak base. In order for a species to have a strong conjugate base it has to be a very weak acid, like water.
The numbers 200-900 would be confused easily with 22 to 29 if they were used in chemistry. khīlioi = 1000, diskhīlioi = 2000, triskhīlioi = 3000, etc. 13 to 19 are formed by starting with the Greek word for the number of ones, followed by και (the Greek word for 'and'), followed by δέκα (the Greek word for 'ten').
The subgroups can thus be divided into conjugacy classes, with two subgroups belonging to the same class if and only if they are conjugate. Conjugate subgroups are isomorphic, but isomorphic subgroups need not be conjugate. For example, an abelian group may have two different subgroups which are isomorphic, but they are never conjugate.
In solution chemistry, it is common to use H + as an abbreviation for the solvated hydrogen ion, regardless of the solvent. In aqueous solution H + denotes a solvated hydronium ion rather than a proton. [9] [10] The designation of an acid or base as "conjugate" depends on the context. The conjugate acid BH + of a base B dissociates according to
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 being real numbers, then its complex conjugate a − bi is also a root of P. [1]
The conjugate transpose of a matrix with real entries reduces to the transpose of , as the conjugate of a real number is the number itself. The conjugate transpose can be motivated by noting that complex numbers can be usefully represented by 2 × 2 {\displaystyle 2\times 2} real matrices, obeying matrix addition and multiplication: a + i b ≡ ...
In chemistry and biochemistry, the Henderson–Hasselbalch equation = + ([] []) relates the pH of a chemical solution of a weak acid to the numerical value of the acid dissociation constant, K a, of acid and the ratio of the concentrations, [] [] of the acid and its conjugate base in an equilibrium.