Philosophy to ponder upon.

What is the philosophy behind COMPLEX NUMBERS and the 'Imaginary' operator i?

I'm thinking. Why is something that is IMAGINARY so pervasive in something as REAL and PRACTICAL as engineering and mathematics?!

For the uninitiated, (FARTs such as terr, ghz and the other pangster; the academic youngsters : jiahui ; the seldom exposed : pok) complex numbers are extremely useful and pervasive in electrical engineering in the least.

Many analyses of engineering systems, models, approximations, require at least some if not complete use of complex numbers. Contrary to what the name seems to imply, complex analysis isn't complex at all! In fact if you tried to do the analysis using real numbers, it would be very difficult, much more difficult than using complex numbers and it might even be impossible! On the other hand using complex numbers, the analysis might even be neatly done in a few lines! If you really can't understand or appreciate the above, well just take my word for it and use your superior intelligence to at least understand this.

How can something imagined, made up, created out of thin air, be so useful and have such concrete results and applications?! Doesn't take much for me to imagine some mathematical quantity but chances are it's just plain rubbish.. yet how did complex numbers come about and actually turn out to be such a great engineering tool?! I'm totally baffled.

Pangy was pricked and bled at 10:53 PM