2007 RJC Prelim H2MA P2 (Qns)

# 2007 RJC Prelim H2MA P2 (Qns) - RAFFLES JUNIOR COLLEGE JC2...

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2 RJC 2007 9740 / 02 / S / 07 Section A: Pure Mathematics [40 marks] 1 (a) The complex numbers z and w are such that z = 3 5i 1 2i a and w = 1+13bi, where a and b are real. Given that z * = w , find the exact values of a and b . [3] (b) Show that    i i 2 e e cos n θ n θ n n w w w a θ w b , where a and b are real numbers to be determined. Hence find the roots of the equation 63 3 1 0 zz   in the form of θ r i e . [6] 2 The following system of linear equations is given: 2 2 4 -----------(1) 2 3 4 1 -----------(2) 4 3 2 -----------(3) x y z x y z x y z    (a) By solving the system of linear equations, comment on the solution of this set of equations and the geometrical representation of the equations. [3] (b) The Cartesian equations of planes 12 and  are given by equation (1) and (2) respectively. Find a vector perpendicular to both the normals of and . [2] Hence, find (i) a vector equation of l , the line of intersection of and . [2] (ii) in the form 1 .
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## This note was uploaded on 08/29/2009 for the course MA 9740 taught by Professor Moe during the Summer '07 term at Singapore Management.

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2007 RJC Prelim H2MA P2 (Qns) - RAFFLES JUNIOR COLLEGE JC2...

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