If $a,b \in \mathbb{C}$ are transcendental over $\mathbb{Q}$ then is $a^b$ necessarily transcendental over $\mathbb{Q}$?

Question

If $a,b \in \mathbb{C}$ are transcendental over $\mathbb{Q}$ then is $a^b$ is necessarily transcendental over $\mathbb{Q}$ ?

In Wiki I found answer is no but I can't cook up an counter example. Please someone provide a counterexample.

Answer 1

No, for instance $e$ and $\log 2$ are transcendantal over $\mathbb Q$, but $$e^{\log 2}=2$$ isn't.

Answer 2

Another one

$$e^{i\pi}=-1$$

$e$ and $\pi$ therefore $i\pi$ are transcendental and not $-1$