In the previous troll hypothesis blog, you would have learned how the troll coefficient links with relative intelligence quotient which has now been proven thus gaining my Ph.D. Well now that it is theory, I can do more work in trolology.

In fact, I already have. I have discovered an complex exponential function which links the troll coefficient to the complex plane:

z(x)=e^iT(x) + 0

Note that 0 was added to show that the real part of the function was 0.

Where e is Euler's number and i is the square root of negative one.

So taking logarithms, we find a trivial formula for iT(x); Log(e^iT(x).

Using the Euler identity, we discover that when T(x) is pi, z(x)=-1. In fact, we could define the function as periodic. So for all T(x) that is an odd coefficient of pi, z(x) is -1. This implies that the exponential function has a limit which is -1.

This means that there is a limit to how high someone's troll coefficient can be. or indeed low.

By the way, the upper limit is positive one. There are also values which lead to 'i' but this is not a value of T(x). So I have discarded them.