>>IMO i is just an extraordinary integer. But if one is prone to abstractions, one may find oneself to think of one (not oneself, but selfless one) as an abstract entity, as abstract as i is. In the concrete case... I don't know what's in that case, the lid is too heavy.
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>i was where I lost interest in mathematics. People with better understanding of math than me have explained that it makes perfect sense but it has never made sense to me.

Complex calculus is among the weirdest things I learned, but it explains a lot of behavior of functions that look anomalous in real numbers (like logarithms of negative numbers etc).

And then I heard from an electrical engineer that the AC circuit resistance is calculated far easier if you take capacitance to be imaginary and inductivity to be the real component. The equations begin to look nice then.

Also, the functions that describe the flow of air around an airplane's wings are quite simple - f(x)=(a*x+b)/(c*x+d) - if all the constants and variables are complex. http://en.wikipedia.org/wiki/Nikolai_Yegorovich_Zhukovsky doesn't say much, though.