## Quick Reference

(of a complex number)

For any complex number *z*, where *z*=*x*+*yi*, its conjugate z̄ (read as ‘*z* bar’) is equal to *x*−*yi*. 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 *z*^{n}+*a*_{1}*z*^{n−1} +⋯+ *a*_{n−1}*z*+*a*_{n}=0, where *a*_{1},…, *a*_{n} are real, then *ᾱ* is also a root of this equation.

*Subjects:*
Mathematics.