Comments on: Intuitive Arithmetic With Complex Numbers http://betterexplained.com/articles/intuitive-arithmetic-with-complex-numbers/ Learning shouldn't hurt. Let's share the insights that made difficult ideas click. Fri, 10 Sep 2010 15:29:12 +0000 http://wordpress.org/?v=2.8.4 hourly 1 By: Kalid http://betterexplained.com/articles/intuitive-arithmetic-with-complex-numbers/#comment-306871 Kalid Sat, 03 Jul 2010 06:39:31 +0000 http://betterexplained.com/articles/intuitive-arithmetic-with-complex-numbers/#comment-306871 @Largo: Oh, I like "twirl" and the video camera analogy -- it gets the idea across! (I love, love, love seeing how other people see these topics). And well, adding is like sliding the camera up and down (moving left/right/up/down is adding numbers in the real or complex plane). Thanks for the kind words, happy you're enjoying the site! @Largo: Oh, I like “twirl” and the video camera analogy — it gets the idea across! (I love, love, love seeing how other people see these topics). And well, adding is like sliding the camera up and down (moving left/right/up/down is adding numbers in the real or complex plane).

Thanks for the kind words, happy you’re enjoying the site!

]]> By: Largo http://betterexplained.com/articles/intuitive-arithmetic-with-complex-numbers/#comment-306546 Largo Wed, 23 Jun 2010 11:54:54 +0000 http://betterexplained.com/articles/intuitive-arithmetic-with-complex-numbers/#comment-306546 Here is a crisp and dynamic word for complex numbers, hand both as a verb and a noun: <b>twirl</i>. I've used it with my eight year old son, thinking of a video camera over a plane that can be both zoomed and rotated. It did not take him long to convince himself that zooms and rotations can be combined, in arbitrary order, without affecting the result. The combination of a zoom and a rotation is a twirl (imagine the twirling trajectory of the point 1+0i). Unfortunately, it is a useful term only for multiplication, not adding. But perhaps that is a feature rather than a bug, helping keep focus on the operations rather than the numbers. May I say that I love this site, and wish I had discovered it before today! :-) Here is a crisp and dynamic word for complex numbers, hand both as a verb and a noun: twirl.

I’ve used it with my eight year old son, thinking of a video camera over a plane that can be both zoomed and rotated. It did not take him long to convince himself that zooms and rotations can be combined, in arbitrary order, without affecting the result. The combination of a zoom and a rotation is a twirl (imagine the twirling trajectory of the point 1+0i).

Unfortunately, it is a useful term only for multiplication, not adding. But perhaps that is a feature rather than a bug, helping keep focus on the operations rather than the numbers.

May I say that I love this site, and wish I had discovered it before today! :-)

]]> By: Dan http://betterexplained.com/articles/intuitive-arithmetic-with-complex-numbers/#comment-274357 Dan Sat, 27 Feb 2010 14:39:09 +0000 http://betterexplained.com/articles/intuitive-arithmetic-with-complex-numbers/#comment-274357 Err, quite elegant for the most part, however I'm hung up on the division. Why do we take the conjugate of the denominator and not the numerator (obviously, algebraically this is obvious, but intuitively?) And why do we WANT to shrink the denominator by its modulus, why not shrink it by 56 or something arbitrary? Err, quite elegant for the most part, however I’m hung up on the division. Why do we take the conjugate of the denominator and not the numerator (obviously, algebraically this is obvious, but intuitively?) And why do we WANT to shrink the denominator by its modulus, why not shrink it by 56 or something arbitrary?

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