Powers of transcendental numbers
I'm having trouble proving that if is transcendent, then and (where is some non-zero rational constant) are transcendental.
I know that if is algebraic, then it is the root of some polynomial, . Then, if this is a linear polynomial in , is it right to conclude that any roots will be in ? If that is the case, can we then set some other polynomial, and conclude a contradiction?
For the other one, if we have is algebraic, then it is the root of . I don't know where to proceed from here, really.
Thank you in advance,