A nice simple identity I obtained in high school learning trigonometry: z^(1/2) = ((z+1)/2)*sin(acos((z-1)/z+1))) for all z ...similar identities may be obtai

A nice simple identity I obtained in high school learning trigonometry: z^(1/2) = ((z+1)/2)*sin(acos((z-1)/z+1))) for all z ...similar identities may be obtained using atan, etc. This came to me from the euclidean geometry construction of sqrt(z). I would like to have its construction image here, but the ascii art is too much. Perhaps Google would find it. When I messed with it, I noticed for large z, acos()--> 1, it's argument describes an angle going to zero and `bends' the left edge of the circle's subtended arc into a vertical line, say, as a zooming magnification. A dynamic screen as yours would be fun to watch the vertex of enclosed right-angle(largest) of the sqrt(z) half-chord, as you mouse drag this vertex around.