#### Answer

If $a+bi$ is a root of a polynomial equation with real coefficients, $b\ne 0$ then $a-bi$ is also a root of the equation.

#### Work Step by Step

According to the properties of roots of polynomial equations, if a polynomial equation with real coefficients has $a+bi$ as one of its roots, where $b\ne 0$, then $a-bi$ must also be a root of that equation. That is, if a polynomial equation has imaginary roots, they must exist in conjugate pairs.