24 8. (i) The point P is one vertex of a regular pentagon in an Argand diagram. The centre of the pentagon is at the origin. Given that P represents the complex number 6 + 6i , determine the complex numbers that represent the other vertices of the pentagon, giving your answers in the form reiθ (5) (ii) (a) On a single Argand diagram, shade the region, R, that satisfies both | z − 2i |  2        and        1 4 π  arg  z  1 3 π (2) (b) Determine the exact area of R, giving your answer in simplest form. (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________