Pearson Edexcel Level 3 GCE. Further Mathematics Advanced PAPER 2: Core Pure Mathematics 2

1. Given that 1 2 3 cos isin 3 3 2 cos isin 12 12 π π z π π z       = +                  = −            (a) write down the exact value of (i) | z1z2 | (ii) arg(z1z2) ...

1. Given that 1 2 3 cos isin 3 3 2 cos isin 12 12 π π z π π z       = +                  = −            (a) write down the exact value of (i) | z1z2 | (ii) arg(z1z2) (2) Given that w = z 1z2 and that arg(wn) = 0, where n  + (b) determine (i) the smallest positive value of n (ii) the corresponding value of | wn | (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________*P66797A0332* Turn over 3 Question 1 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 1 is 5 marks)4 *P66797A0432* 2. A = 4 2 5 3  −    The matrix A represents the linear transformation M. Prove that, for the linear transformation M, there are no invariant line