page 06 MARKS 10. Given z x iy = + , sketch the locus in the complex plane given by z z i = − + 2 2 . 11. (a) Obtain the matrix, A, associated with an anticlockwise rotation of π 3 radians about the origin. (b) Find the matrix, B, associated with a reflection in the x-axis. (c) Hence obtain the matrix, P, associated with an anticlockwise rotation of π 3 radians about the origin followed by reflection in the x-axis, expressing your answer using exact values. (d) Explain why matrix P is not associated with rotation about the origin. 12. Prove by induction that, for all positive integers n, ( ) n r n r − = = − ∑ 1 1 1 3 3 1 2 . 3 1 1 2 1 5