Is it standard to say -i\log(-1) is \pi?

Kaiya Hardin

Kaiya Hardin

Answered question

2022-04-28

Is it standard to say ilog(1) is π?

Answer & Explanation

prstenast4yi

prstenast4yi

Beginner2022-04-29Added 12 answers

It is not which 1 but which log which is the issue. Wolfram Alpha has used some kind of principal value of the complex logarithm. But using this, alog(b)=log(ba) is no longer always true.
Deandre Barron

Deandre Barron

Beginner2022-04-30Added 17 answers

The (principal value) of the complex logarithm is defined as
logz=ln|z|+iArg(z).
Therefore,
log(1)=ln|1|+iArg(1)=0+iπ.
and then, one simply gets
ilog(1)=i(iπ)=π.

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