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(of a complex number)

For any complex number z, where z=x+yi, its conjugate z̄ (read as ‘z bar’) is equal to xyi. In the complex plane, the points representing a complex number and its conjugate are mirror images with respect to the real axis. The following properties hold:It is an important fact that if the complex number α is a root of a polynomial equation zn+a1zn−1 +⋯+ an−1z+an=0, where a1,…, an are real, then is also a root of this equation.

Subjects: Mathematics.

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