Jimbo,




You misunderstood my statement. I myself wrote :"this math structure we humans are able to solve many complicated problems". Sound like "... actual real world physical phenomena described well by complex numbers ... " to me.

What I was referring to is that an imaginairy number has no meaning in the real world. Example. If a wave has a frequency of say 10 Hertz that we know what that physically means. If however a wave has a frequency of say (10 + 4J) (= imaginairy number, with the J identifying the imaginairy part and the 10 being the real part) than nobody knows what that means in physical terms. Nor does such a wave form exist in the real world or can ever be made to exist. Such a construction that is very much possible in mathematical terms, is simply non-existant (impossible) in the real world where ONLY REAL numbers exist. That is why I say that an imaginairy number is just plain BS in the real world. It is as concrete in the real world as little wood elfs.

Did I loose any of the other guys yet ? Yep we are talking about imaginairy numbers, no kidding they really do exist in mathematics and are quite helpful, especially in the analysis of oscillating systems.

So for you guys the answer to how can imaginairy numbers be helpful in real life problems ? Because any system that initially is worded in real valued equations will produce real valued answer even though the path in between is using imaginairy numbers. In such a case the imaginairy numbers occur in what is called complex conjugate pairs. Example : whenever the number 10 + 4j arises than somewhere else its mirror image 10 - 4j arises as well; that is when the original problem is real valued. The math structure around these numbers keeps the pair linked to one-another so they constantly are added/subtracted or multiplied with eachother. Often right before the final sought after answer, which always is a value with meaning in the real world, the two mirror images are added or multiplied by one another resulting in a real valued number.

example : (10 + 4j) + (10 - 4j) = (10 + 10) + (4j - 4j) = 20 + 0J = 20 = real value.

Similar thing happens when multiplying to mirror complex numbers.

The structure that enforces this behaviour is linked to wether a problem exist in the real world. If the final answer is NOT a real value then either you have made a calculation error or the original problem you were analysing simply does NOT exist in the real world.

Funny stuff this is, right ?

Who said Mathematics are boring ? The further you get into studying mathematics to more wild the phenomenons get. You just need a good teacher to get through the basics after that it gets mind blowing

Wouter