It's from the 2008 CSSA Trial.
2 (e) The points O, A, Z and C on the Argand diagram represent complex numbers 0, 1, z and z+1 respectively, where z = cos@ + isin@ is any complex number of modulus 1, with 0 < @ < pi.
(i) Explain why OACZ is a rhombus.
(ii) Show that (z-1)/(z+1) is purely...