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What is the value of $1^i$? - Mathematics Stack Exchange

Aug 30, 2010 · There are infinitely many possible values for $1^i$, corresponding to different branches of the complex logarithm. The confusing point here is that the formula $1^x = 1$ is not part of the definition of...

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Why is $1/i$ equal to $-i$? - Mathematics Stack Exchange

May 11, 2015 · 11 There are multiple ways of writing out a given complex number, or a number in general. Usually we reduce things to the "simplest" terms for display -- saying $0$ is a lot cleaner than saying $1-1$ fo...

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为什么 1 不能被认为是质数? - 知乎

质数就是“只能被1和它本身整除”的自然数。 然而,我们必须在此基础之上增加一条警告,宣称数字1不是质数,这简直就像马后炮一样。

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Why is $1$ not a prime number? - Mathematics Stack Exchange

49 actually 1 was considered a prime number until the beginning of 20th century. Unique factorization was a driving force beneath its changing of status, since it's formulation is quickier if 1 is not considered a pri...

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factorial - Why does 0! = 1? - Mathematics Stack Exchange

The theorem that $\binom {n} {k} = \frac {n!} {k! (n-k)!}$ already assumes $0!$ is defined to be $1$. Otherwise this would be restricted to $0 <k < n$. A reason that we do define $0!$ to be $1$ is so that we can cover...