Talk:Quater-imaginary base

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Can someone explain why this is spelled "quater-imaginary" instead of "quarter-imaginary"? What does "quater" mean?

It's a Latin adverb meaning "four times" (i.e. once beyond thrice). I would guess that it refers to the fact that the system can cover all four quadrants of the complex number system with a single numerical representation. AnonMoos 15:42, 23 February 2006 (UTC)
Actually, it's because the system uses four different digits. -- Milo

Contents

[edit] Non-standard positional numeral systems

I have addressed certain issues by creating the article Non-standard positional numeral systems, and making related changes to Unary numeral system, Golden ratio base, Quater-imaginary base, Positional notation, Base (mathematics), and Category:Positional numeral systems. I suggest further discussion of these issues takes place at talk:Non-standard positional numeral systems.--Niels Ø 14:32, 26 February 2006 (UTC)

[edit] Unique?

Spending just a minute looking at this, it appears that this system uniquely represents any complex number (no number has more than one representation). Is there a proof of this around? I think it would be good to include. If it doesn't, a counterexample would be nice too. Hjfreyer 12:52, 9 February 2007 (UTC)

Sadly, no. 1.0300(0300)... = 1/5 = 0.0003(0003)... Note that, as with 1.000... and 0.999... in base 10, these are respectively the smallest and largest numbers representable with integral part 1 and 0 respectively. –EdC 21:37, 19 April 2007 (UTC)

[edit] New section

This article really should have a “Quater-imaginary to decimal” section. — Ti89TProgrammer 04:28, 1 August 2007 (UTC)

[edit] Added Examples etc.

I added two sections on converting to and from the quater-imaginary system. I also added sections on adding, subtracting and multiplication, with examples. I haven't done division, because I don't (yet) know how this works (anyone?). I also changed the "powers of 2i" table to a horizontal table for readability. -GjjvdBurg (talk) 15:38, 21 December 2007 (UTC)

[edit] 10i-base equivalent

Is it worth mentioning that a similar system can be made using 10i as the base, which is similarly able to represent every complex number using only the digits 0 through 9 without a sign (but which may be slightly more comprehensible to novices)? — Loadmaster (talk) 05:06, 24 December 2007 (UTC)

Sure, it would be alright to add some links to other numeral systems but I think a system with base 10i should have a separate article (if it isn't already there). -GjjvdBurg (talk) 11:31, 25 December 2007 (UTC)
This doesn't actually work; for base ni you need n2 digits, not n, which makes the whole thing impractical (if it wasn't already) for n much beyond 4. For n = 3 there are a couple of nice balanced systems with digit values of −4, −3, ..., 3, 4 and {0,±1} + {0,±1} i. Actually for the latter you don't need base 3i; base 3 works just as well. -- BenRG (talk) 21:07, 4 February 2008 (UTC)

[edit] difference in notation

hello, It's a mistake to use an 'x' as the multiplication sign in the first two formulas and a dot in the rest, there should be only one way to express this instead of two because it might lead to think that they have different meanings and (afaik) it's not the case. Samus_ (talk) 20:25, 20 January 2008 (UTC)