Is it an open problem about Riemann Hypothesis non-trivial zero?

Question

Let's assume RH was correct, and $1/2+Ki$ is any one of non-trivial zero of $\zeta$, is following problem open?

1) $K$ is irrational number

2) $K$ is transcendental number

Answer 1

The problems are still open as currently no one knows what $K$ is: either irrational number or transcendental number.