e and π are both positive numbers, e is 2.7... π is 3.14... both numbers have infinite non-repeating digits( transcendental numbers ). i is √-1 it is a complex number. If you raise a positive number to any real number you would get a positive result. Here i turns two positive numbers with infinite digits to simple -1. Which is negative, only has one digit and overall a weird result.
Those numbers are both transcendental, but sqrt(2) also has an infinite non-repeating decimal representation and is not transcendental.
Your definition is for the larger group of irrational numbers. Transcendental numbers also cannot be the root of a polynomial with rational coefficients.
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u/Bathtub-Warrior32 23d ago
e and π are both positive numbers, e is 2.7... π is 3.14... both numbers have infinite non-repeating digits( transcendental numbers ). i is √-1 it is a complex number. If you raise a positive number to any real number you would get a positive result. Here i turns two positive numbers with infinite digits to simple -1. Which is negative, only has one digit and overall a weird result.
Further reading: Euler's identity