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Prove that $\pi=2i\ln\left(\frac{1-i}{1+i}\right)$

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#solution-verification #logarithms #transcendental-numbers
101
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If the algebraic expression of a transcendental number is algebraic, is the number algebraic?

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#field-theory #transcendental-numbers
69
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Does an algebraic irrational number always have all digits from the base?

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#irrational-numbers #transcendental-numbers
110
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Proof of $e$ is transcendental

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#elementary-number-theory #transcendental-numbers
63
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Necessary and sufficient condition for a number to be algebraic

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#real-analysis #number-theory #elementary-number-theory #irrational-numbers #transcendental-numbers
98
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An "easy" way to get $\ln 7$ from $\ln 2$?

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#abstract-algebra #extension-field #transcendental-numbers
48
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automorphism between transcendental elements

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#abstract-algebra #ring-theory #field-theory #transcendental-numbers
133
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Does reinterpreting the base of a number leave transcendence unchanged?

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#number-theory #reference-request #transcendental-numbers
123
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Are angles of Pythagorean triples, e.g. $\tan^{-1}\frac34$, transcendental multiples of $\pi$?

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#number-theory #trigonometry #transcendental-numbers
360
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Criteria for irrationality of Euler's constant

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#real-analysis #number-theory #irrational-numbers #transcendental-numbers #euler-mascheroni-constant
45
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transcendental numbers as solutions to hyperpowers

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#transcendental-numbers
109
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Why a root for an integer polynomial in definition of transcendental number?

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#transcendental-numbers
58
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House of the inverse

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#algebraic-number-theory #transcendental-numbers #transcendence-theory
593
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How to identify transcendental numbers?

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#field-theory #transcendental-numbers
127
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Does a transcendental number raised to the power of an irrational algebraic number, always result in an algebraic number?

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#exponentiation #irrational-numbers #transcendental-numbers

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