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A New High in Teaching Mathematics
Aubrey, who has started this evening to learn Python, suddenly came to me asking what is abs(). I looked at her puzzled for a couple of seconds and realised that she had discovered the native Pythonic support for complex numbers in the online documentation. I had already explained to her what complex numbers are several times in the past and knew that the classical approach would not work. That's when I had a brilliant idea which lead to the following

Pascal: You know what numbers are right ? Ok, so take two of them. The first one will be the husband and the second one will be the wife, and together they are a married couple. That's a complex number. A complex number is two numbers having got married. For instance if you take 3 and 5, then 3 is the husband and 5 is the wife and then (3,5) is the resulting couple, the resulting complex number.

Aubrey: Right, but what about the "j" ?

Pascal: The "j" is Python's way to say which of the two in the wife.

Aubrey: Ok, I get it, but then in "3+4j" the plus is not really a plus right ?

Pascal: (Thinking: "Oh shit, I don't like the way all this is going because if I said no, then how am I going to justify algebraic operations on complex numbers.. Well..., never mind"). No darling, the plus is not really a plus.

Aubrey: Ok, so "abs" ?

Pascal: Ha, yes. So after having got married, the two numbers need a place to stay, and they go to town and their home is the point on the cartesian plan which is defined by themselves. For instance the couple/complex number 3+4j is going to live in an house at position (3,4). 3 on the x-axis and 4 on the y-axis. Then abs is how far away their house is from the city center, represented by the point (0,0).

Aubrey: Ha yes, that's 5, because I remember once you told me about 3 and 4 and squares, and there was Pythagorus somewhere and I know that it's 5 !

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