Cube root of a complex

There are three cube roots of a complex number. These can be found by looking for the numbers that when cubed yield and. These... 

Humans excel at some types of task We can recognize the face of a friend almost instantly, even though the computations in the brain required to do so are complex. On the other hand, humans are not very adept at mathematical tasks Although a computer could cube root 373232448215999 in milliseconds, few people could do this at all without the aid of pencil and paper or calculator, let alone manage it in less than a second. 

Thus the only way to make a complex is to transfer some of the internal energy to another system. In practice, this means three or more molecules have to all be close enough to interact at the same time. The mean distance between molecules is approximately (V/N)1 /3 (the quantity V/N is the amount of space available for each molecule, and the cube root gives us an average dimension of this space). At STP 6.02 x 1023 gas molecules occupy 22.4 L (.0224 m3) so (V/N)1/3 is 3.7 nm—on the order of 10 molecular diameters. This is expected because the density of a gas at STP is typically a factor of 103 less than the density of a liquid or solid. So three-body collisions are rare. In addition, if the well depth V (rmin) is not much greater than the average kinetic en-... 

The Riemann surface for the cube root f(z) = z comprises three Riemann sheets, corresponding to three branches of the function. Analogously, any integer or rational power of z will have a finite number of branches. However, an irrational power such as f(z) = z = will not be periodic in any integer multiple of In and will hence require an infinite number of Riemaim sheets. The same is true of the complex logarithmic function... 

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