Lots of powers

For every pair of complex numbers a and b, provided a is not 1 and neither a nor b is 0, there exists a complex number c such that a^c = b. In other words, there is a number c such that b is the cth power of a. Another way of putting this is that there is a number c such that a is the cth root of b. 

Given a and b, we can find c simply by calculating (ln b)/(ln a). Of course (?) the natural log function ln z is multivalued, so there will actually be an infinite number of solutions. If we want just one, we can use the formula c = (Ln b)/(Ln a), where Ln z is the principal value of the complex logarithm.

Division ±mod 11

OK, I've waited too long. Here's an example of modular division with a prime modulus, i.e., 11. By way of reference I also include the multiplication table. I have replaced 6, 7, 8, 9, and 10 with their negative values: –5, –4, –3, –2, and –1, respectively.

I won't attempt to explain this or comment on it, other than saying I think it's beautiful.