For starters, you have good teachers. It is impossible to understand without knowing. I mean, just giving strategies how to pass is bad. Let's face it, if I explain how to derive simple polynomials to a third grader; honestly, he will probably do it better then me. At the same time, sometimes you have to do hundreds of examples until the train though begins to run smoothly.
It's like about that question with negative numbers. I mean, if you really think about it - they don't exist! People were having a hard time to accept something "negative" until like 14th century. With modern economy, we are all pretty much used to something of a "negative" quantity. Same applies with complex numbers. I mean, in my domain, we use them all the time; they make electrical engineers life so much easier. It becomes trivial, so I can focus on other things. I mean, if you would stop and focus on the fact that root of two doesn't exist every time you solve a quadratic - you wouldn't get far.
PS Hm... I don't know to be honest. I am pretty sure there is something fishy about this whole Pi idea... seems a bit artificial to me. Nature almost never creates perfect circles... maybe because too many people talk about it? My dentist seem to know a bit more, so he always starts by Pi, then mentions the golden ration and finishes with complex numbers and how it is all bizarre... the conversation typically ends with something like: "e is the way to go if you ask me."
Edited by Roman Pope, 28 June 2009 - 12:37 AM.
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