I'm slightly confused on the subject of conjugates and how to define them.
I know that for a complex number $ a - bi $ the conjugate is $ a + bi $ and similarly for $ 1 + \sqrt 2 $ the conjugate is $ 1 - \sqrt2 $ because when multiplied it gives a rational answer.
But how about for just a simple real number like 1 or 2, what would be the conjugate for this? Does a conjugate exist for a real number?
I'm new to this topic and have tried searching Maths SE and Google in vain; any help would be appreciated.