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**mHadad** well as i know about Digital Signal Processing as i'm yet a begginer in that science that i have seen a usage for complex numbers where they call it ,the imaginary part.i think it was used in convolution.but what i meant by a real world example is that u raise a unit of time by the power of 2 then take the square root of it so it can not be negative or you subtract one point from another in a coordinate plane then raise the result by 2 then take the square root of it to get the absolute value ,like in the distance formula:

d(a,b) = sqrt. ( ( x2 - x1 ) ^ 2 + ( y2 - y1 ) ^ 2 )

but i can not say that i can understand a real world incident by i^2 = -1 ,unless it means something like the following : imagine a rubber band that is held between the two fingers for example.if i apply a pressure againset it ,as i'm increasing my pressure it's resistance(the rubber band) will decrease (to a certain point ,which is denoted by the negative number for example).mmm that what came into my mind while typing ,don't know if it holds true or not because what if i increase the pressure againset this rubber band then what is the power of i and does it have to continue to be negative?

correct me if i'm wrong.