Hi, I tried to find out how to plot a pentagram in the complex plane. Let the radius of the pentagram be 1, then all the corners of the pentagram satisfy the equation x^5 = 1 (where x is a complex number). The answer is, of course, x = exp (2n*pi*i/5). But I wanted to express that in roots, not in exponentials. I could not find anything on the Web, so I tried it myself. It can be done, but the answer is not beautiful. The prime root is: x = a + i*a / sqrt(1-2/sqrt(5)), where a = [ (9-4*sqrt(5)) / (16*sqrt(5)-16) ]^(1/5). Next, I tried to express this in terms of the "Golden Ratio" Phi. Because I knew that Phi appears in the pentagram a lot. Since Phi^2 = 1*Phi + 1 Phi^3 = 2*Phi + 1 Phi^4 = 3*Phi + 2 Phi^5 = 5*Phi + 3 ... and so on (that's the Fibonacci series twice), we get x = (Phi - 1)/2 + sqrt(Phi + 2)*i/2 and also x^2 = -Phi/2 + sqrt(-Phi + 3)*i/2. (x^3 and x^4 are obviously symmetrical wrt. the real axis) That looks better. But not perfect. I tried to get rid of the square root in the imaginary part, because I wanted everything to be linear in Phi. But no success. Any help?