What is a complex conjugate?

Answer 1

For a and b real, the conjugate of a + bi is a - bi.

The cool thing is that the conjugate of a sum or product is the sum or product of the conjugates.

Answer 2

For a polynomial with real number coefficients, complex roots always come in conjugate pairs.

So for some polynomial f(x) = ax^3 + bx^2 + cx + d, if you're given that (4 + i) is a root, it follows that its conjugate, (4 - i), must also be a root.

The conjugate of a complex number (m + ni) is (m - ni), and vice versa.