std.complex

[Lars T. Kyllingstad]

On Thursday, 2 January 2014 at 23:26:48 UTC, Joseph Rushton 
Wakeling wrote:
> On 02/01/14 23:26, Lars T. Kyllingstad wrote:
>>>   * You can do calculations involving purely real-valued 
>>> numbers and complex
>>>     numbers and not run into the same issues, because purely 
>>> real values are
>>>     supported. So you should be able to do the same with 
>>> purely imaginary
>>>     numbers.
>>
>> That argument is fallacious. Imaginary numbers are quite 
>> different from real
>> numbers.
>
> Can you expand on that?

Mathematically, the real numbers are a ring, whereas the purely 
imaginary numbers are not. (I've been out of the abstract algebra 
game for a couple of years now, so please arrest me if I've 
remembered the terminology wrongly.)  What it boils down to is 
that they are not closed under multiplication, which gives them 
radically different properties - or lack thereof.