Questions Further AS Paper 1 (126 questions)

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AQA Further AS Paper 1 2020 June Q18
5 marks Standard +0.8
The locus of points \(L_1\) satisfies the equation \(|z| = 2\) The locus of points \(L_2\) satisfies the equation \(\arg(z + 4) = \frac{\pi}{4}\)
  1. Sketch \(L_1\) on the Argand diagram below. \includegraphics{figure_18} [1 mark]
  2. Sketch \(L_2\) on the Argand diagram above. [1 mark]
  3. The complex number \(a + ib\), where \(a\) and \(b\) are real, lies on \(L_1\) The complex number \(c + id\), where \(c\) and \(d\) are real, lies on \(L_2\) Calculate the least possible value of the expression $$(c - a)^2 + (d - b)^2$$ [3 marks]