The complex number 2i is denoted by u. The complex number with modulus 1 and argument \(\frac{2}{3} \pi\) is denoted by w.

(i) Find in the form x + iy, where x and y are real, the complex numbers w, uw and \(\frac{u}{w}\).

(ii) Sketch an Argand diagram showing the points U, A and B representing the complex numbers u, uw and \(\frac{u}{w}\) respectively.

(iii) Prove that triangle UAB is equilateral.