(a) The complex numbers z and w satisfy the equations

\(z + (1+i)w = i\)

and

\((1-i)z + iw = 1\).

Solve the equations for z and w, giving your answers in the form x + iy, where x and y are real.

(b) The complex numbers u and v are given by \(u = 1 + (2\sqrt{3})i\) and \(v = 3 + 2i\). In an Argand diagram, u and v are represented by the points A and B. A third point C lies in the first quadrant and is such that \(BC = 2AB\) and angle \(\angle ABC = 90^\circ\). Find the complex number z represented by C, giving your answer in the form x + iy, where x and y are real and exact.