The question:

Use the properties of the complex conjugate to show that if the complex number 'z' is a root of a quadratic equation with a, b, c being real coefficients, then so is the conjugate of 'z'.

My attempt:

Let z =

Basically, I changed the quadratic formula to look like a complex number in Cartesian form. Is this an acceptable answer? My textbook doesn't have solutions for 'show' and 'prove' questions.

Thanks!