newRPL: The complexity of complex mode
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08-28-2016, 06:33 PM
Post: #11
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RE: newRPL: The complexity of complex mode
(08-28-2016 12:21 AM)Vtile Wrote: It seems I still get definition that says that ATan(inf/inf)=Pi/4 which is not defined (ie. in wolfram alpha), yet \( \mathit{z}=\infty*e^{\frac{i\pi}{4}}\) seems to be legit. The above is precisely why I don't think rectangular representation is "lossless". You lost a lot of information the moment you distributed that infinity into each component of the complex (that operation is invalid, infinity doesn't distribute). If instead of Infinity you had X, the result would be the complex (X*a,X*b). The limit when X tends to infinity would keep the direction of (a,b) as X goes from 0 to infinity, hence the correct result is a vector of infinite length and the same direction of (a,b). This is easy to represent in polar coordinates, hard to do in rectangular. In polar coordinates, you can do the complex multiplication without applying the distributed property that doesn't work with infinity: \(\infty==>\infty*e^{i 0}\) \(Z ==> (a,b) ==> r * e^{i \theta}\) \(\infty*Z = \infty*r * e^{i(0+\theta)} = \infty * e^{i \theta}\) This is why it's best to store a directed infinity in polar form. |
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Messages In This Thread |
newRPL: The complexity of complex mode - Claudio L. - 08-19-2016, 03:44 PM
RE: newRPL: The complexity of complex mode - Nigel (UK) - 08-21-2016, 06:46 AM
RE: newRPL: The complexity of complex mode - Claudio L. - 08-22-2016, 12:45 AM
RE: newRPL: The complexity of complex mode - Nigel (UK) - 08-22-2016, 03:03 PM
RE: newRPL: The complexity of complex mode - Claudio L. - 08-23-2016, 07:43 PM
RE: newRPL: The complexity of complex mode - Nigel (UK) - 08-24-2016, 10:32 AM
RE: newRPL: The complexity of complex mode - Claudio L. - 08-25-2016, 02:39 AM
RE: newRPL: The complexity of complex mode - Vtile - 08-24-2016, 04:06 PM
RE: newRPL: The complexity of complex mode - Claudio L. - 08-25-2016, 03:09 AM
RE: newRPL: The complexity of complex mode - Vtile - 08-28-2016, 12:21 AM
RE: newRPL: The complexity of complex mode - Claudio L. - 08-28-2016 06:33 PM
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