What is the complex conjugate?

The complex conjugate of a complex number is a number for which the real part is the same and for which the imaginary part has the same magnitude but opposite sign. e.g. the complex conjugate of 6+7i is 6-7i. It should be noted for a polynomial with real coefficients that complex roots come in complex pairs. So if the complex number is a root, its conjugate will be as well.