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Topic: What's the geometry meaning of i^i ?
Replies: 16   Last Post: Jul 29, 2012 2:34 PM

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Richard Tobin

Posts: 1,436
Registered: 12/6/04
Re: What's the geometry meaning of i^i ?
Posted: Jul 26, 2012 6:27 PM
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In article <junsli$7n8$>,
Hongyi Zhao <> wrote:

>What's the geometry meaning of i^i ? Here, i is the imaginary unit.

We can naturally define b^x as e^(x log b). The principal value of
log i is pi/2 i, so i^i is e^(-pi/2).

All you need now is a geometric interpretation of log i. For an
imaginary number the log is i times the phase, but I'm not sure
that is really an interpretation.

-- Richard

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