The complex numbers and satisfy the equation z w (2 + i)(z + 3i) = w (c) Use algebra to find giving your answer in the form + z, a bi, where and are real numbers. a b (4) Given that arg(λ + 9i + = w) where is a real constant, λ (d) find the value of λ. (2) 10. (i) Use the standard results for and to evaluate (2) (ii) Use the standard results for and to show that for all integers 0, where and are constant integers to be found. n a, b c ≥ (6) TOTAL FOR PAPER: 75 MARKS END Paper Reference(s) 6667/01 Edexcel GCE Further Pure Mathematics FP1
The complex numbers z and w satisfy the equation (2 + i)(z + 3i) = w (c) Use algebra to find z, giving your answer in the form a + bi, where a and b are real numbers. (4) Given that arg(λ + 9i + w) = where λ is a real constant, (d) find the value of λ. (2) 10. (i) Use the standard results for and to evaluate (2) (ii) Use the standard results for and to show that for all integers n ≥ 0, where a, b and c are constant integers to be found. (6) TOTAL FOR PAPER: 75 MARKS END Paper Reference(s) 6667/01 Edexcel GCE Further Pure Mathematics FP1