konjugáltak

In mathematics, "konjugáltak" is the Hungarian term for conjugates. This concept appears in various areas of algebra, most notably with complex numbers and algebraic integers.

For complex numbers, the conjugate of a complex number a + bi is a - bi, where 'a' is the real part and 'b' is the imaginary part. This operation is often denoted by a bar over the number or an asterisk. For example, the conjugate of $z = 3 + 2i$ is $\bar{z} = 3 - 2i$. Conjugation has useful properties, such as the product of a complex number and its conjugate being a non-negative real number ($z\bar{z} = a^2 + b^2$).

The concept of conjugates also extends to algebraic numbers. An algebraic number is a root of a polynomial with rational coefficients. The conjugates of an algebraic number are the other roots of that same minimal polynomial. For instance, if a number $\alpha$ is a root of a polynomial, its conjugates are all the other distinct roots of that polynomial. Understanding these conjugates is crucial in algebraic number theory for studying the structure of number fields.

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