Question

Which of the following is transcendental number?
(a) e and π
(b) i and e
(c) Φ and Ψ
(d) α and β

Answer 1

option no. a is the answer
hope It would help u☺

Answer 2

Concept

A transcendental number is a number that cannot be solved algebraically because it does not have rational-number coefficients. All irrational numbers are not transcendental, but transcendental numbers are irrational. For instance, the solution to the equation x² - 2 = 0 is x = Square root of 2, which makes the irrational number Square root of 2 an algebraic number and not a transcendental one.

Given

transcendental number

Find

we are asked to identify the transcendental number from the given options.

Solution

A transcendental number in mathematics is a number that is not algebraic, or not the root of a non-zero, finite-degree polynomial with rational coefficients. e and are the two most well-known transcendental numbers.

We show that is not algebraic in order to demonstrate that it is transcendental. The Lindemann-Weierstrass theorem states that e^πi= 1 is transcendental, which is incongruous if is algebraic because I would also be algebraic if were. So, since is not algebraic, it must be transcendental.

hence e and π is transcendental number.

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