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NNTP-Posting-Date: Sat, 10 Sep 2016 13:33:08 -0500
From: Gareth Owen <gwowen@gmail.com>
Newsgroups: comp.lang.c
Subject: Re: The truth comes out ... DNA proves evolution is a myth
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Date: Sat, 10 Sep 2016 19:33:07 +0100
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David Brown <david.brown@hesbynett.no> writes:

> On 10/09/16 07:38, Gareth Owen wrote:
>> David Brown <david.brown@hesbynett.no> writes:
>>
>>>>
>>>> Well nitpicked, sir!
>>>>
>>>
>>> I should probably have added a smiley - after all, it's fairly obvious
>>> that you already know that all real numbers are complex numbers.
>>
>> I read it as with a smiley.  And replied in kind.
>>
>>> Any thoughts on letting n be a Gaussian integer?
>>
>> Off the top of my head it would seem unlikely.  for integer m,n then
>> m^ni will tend to have real and imaginary parts that are irrational
>> (multiples of cos n and sin n) which is going to make balancing
>> contributions unlikely.
>
> Yes, I agree (after having thought about it a bit more).  I guess I'll
> just have to write a test program some time and try it for a small
> range of integers.

Well, the other thing to note if you do that, z^complex is not a
single valued function unless you specify where on the Riemann sheet
you're putting your line of discontinuity:

1^i = (e^0)^i = 1;

But its also

1^i = (e^(2πi))^i = e^(-2π)

and
1^i = (e^(4πi))^i = e^(-4π)
and
1^i = (e^(-4πi))^i = e^(+4π)
and so on.
And there's nothing special about 1^i
The function z^i has infinitely many plausible values, stacked on top of
each other like a multi-level parking garage, and each time you wind
around the origin you pass on to the next level up.