https://www.gregmat.com/quizzes/quiz/prepswift-quant-tickbox-quiz-3-arithmetic-column-3 (Question 16)
I’m not sure on why it’s being asked about transcedental numbers. The examples provided are, indeed, real, but transcedental numbers don’t need to be real.
A good example -which chatgpt provided- is \pi*i. The argument is very easy to follow:
(1) The ratio of two non-transcedental numbers ir non-transcedental,
(2) Suppose that the non-real number \pi*i is non-transcedental.
(3) Since the number ‘i’ is algebraic (it’s the solution of x^{2}+1), the number (\pi*i)/i = \pi is algebraic.
(4) However, \pi is well-known to be a transcedental number.
I know that the examples (\pi and e) are real numbers, but should I awnser based only the examples the question gave?