The points O, I, Z and P on the Argand Plane represent the complex numbers
0, 1, z and z + 1 respectively, where z = cosθ + i sinθ is any complex number of
modulus 1, with 0 <θ <π .
(i) Explain why OIPZ is a rhombus.
(ii) Show that (z-1)/(z+1) is purely imaginary.
(iii) Find the modulus...