**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 !