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#1 2005-09-04 18:50:26

delta_luca
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round, floor and ceil for complex numbers

for complex numbers, is the round/floor/ceil of the complex number the round/floor/ceil of each part
i.e. [3.7+4.2i] = 4+4i

or is it the complex number whos length is the round/floor/ceil of the originals length
i.e.

[3.7+4.2i] = [ |3.7+4.2i| ] * (3.7+4.2i)/|3.7+4.2i| = 3.966+4.502i

Last edited by delta_luca (2005-09-04 18:51:57)

#2 2005-09-04 22:04:21

MathsIsFun
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Re: round, floor and ceil for complex numbers

I don't know for sure. 

For rounding I would suggest that you go with the simpler option, as it yields results that are more usable arithmetically. After all, the rounding function has the effect of reducing accuracy with the tradeoff being ease of use, so you could follow the same philosopy with the complex numbers.

I am not so sure about floor and ceiling, because they can be used in accurate calculations.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

#3 2005-09-05 01:53:43

kylekatarn
Power Member

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Re: round, floor and ceil for complex numbers

I don't know for shure either, but the simpler approach seems more logical.

[x+yi]=[x]+[y]i

#4 2005-09-05 07:43:57

delta_luca
Novice

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Re: round, floor and ceil for complex numbers

ill do some more research and try to find out exactly which is it is: here is my calculator so far, its made in flash and deals with complex numbers: it isnt yet finished but it will also have a graphics side for plotting real graphs and complex graphs(3d):

http://img146.imageshack.us/my.php?image=calculator3jq.swf   (round, ceil and floor obivously aernt working yet, nor is memory allocation or equation navigation and editing, everything else should work fine)

syntax for obscure functions:

logz finds the log of the number to base z, its syntax is:
"base logz number" - for example the log of 3.5 to base (-4+5.51i) would be
(-4+5.51i) logz 3.5

zroot finds the z'th root of the number, syntax is:

"root zroot number" - for example the (3+4i)'th root of 5 would be
(3+4i) zroot 5



here are some renderins (in beta) for the graphics side: the engine im using is not the one that i will use for the proper renderings as this engine uses cameras which obviously slows things down alot - to see them properly and at a good enough speed youll need flash player 8/beta

http://img372.imageshack.us/my.php?image=graphics7vz.swf
(y = re[sin(z)]/20 )

http://img398.imageshack.us/my.php?image=graphics4wl.swf
(y = re[ z^conj(z) ]/40 )

http://img378.imageshack.us/my.php?image=graphics9yx.swf
(y = mod((z^conj(z)) / (e^z)) /40 )

Last edited by delta_luca (2005-09-05 08:19:41)

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