A well-known theorem, due to C.\,J. Smyth, asserts that two conjugates of a Pisot number, having the same modulus are necessary complex conjugates. We show that this result remains true for $K$-Pisot numbers, where $K$ is a real algebraic number field. Also, we prove that a $j$-Pisot number, where $j$ is a natural number, can not have more than $2j$ conjugates with the same modulus.