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Comment Re:I went one further (Score 1) 1260

It is true that sqrt(1) = 1 if you are using the principle square root function, but you only specify that later, not in the "proof". I was merely trying to point out that you were wrong when you said that for a=a to imply that sqrt(a)=sqrt(a) we need to take the principle square root. There are two possible roots, one where we do have that sqrt(x^y) = x^(y/2)(ie. sqrt(i^4) = i^2)and one where sqrt(1) = 1.

I am not trying to say that you were wrong, obviously the problem is with the sqrt step. It's just that the way you put it seemed misleading, at least to me. What I was trying to say is that it is not necessary to assume that sqrt is the principle square root function. I probably should have written something like "There is actually nothing wrong with taking the general square root of a complex number".

Also, I never said that i^4 is imaginary ;) .


Micro-Projectors May Bring YouTube On-The-Go 143

An anonymous reader writes "A tiny portable projector, about the size of a pack of cards, may soon replace a ring tone as the most annoying thing on the train or bus. These technical innovations can project an image up to 50 inches in size in dark lighting, making them ideal for on-the-road business presentations. They can also be hooked up to cell phones or media devices, though, possibly introducing a whole new level of social intrusion into US culture. 'Digital projectors were once bulky. These new models, though, are small enough to fit into the pocket of consumers who want a big-screen experience from a small-screen device. Some of the models are expected to be on the market by year-end, or sooner. Prices have yet to be announced. Matthew S. Brennesholtz, an analyst at Insight Media, a marketing research firm in Norwalk, Conn., says he thinks the projectors will initially cost about $350, then quickly drop to less than $300.'"

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In any formula, constants (especially those obtained from handbooks) are to be treated as variables.