Complex conjugate root theorem
A common intermediate step is to present a complex root of a real polynomial without its conjugate. It is then up to the solver to recognize that its conjugate is also a root.
Let have the form , where constants are real numbers, and let be a complex root of . We then wish to show that , the complex conjugate of , is also a root of . Because is a root of , Then by the properties of complex conjugation, which entails that is a root of , as required.