A2 June 2023 Paper 1 Q13

OCR MEICurrent spec14 marksComplex NumbersGraphs & Inequalities

13

(a) On the separate Argand diagrams below, show the set of points representing each of the following inequalities.
(i) \(|z| \leqslant \sqrt{5}\)
Argand diagram grid from the Printed Answer Booklet: Re axis from -8 to 8 and Im axis from -8i to 8i, with unit grid squares
[3]
(ii) \(|z + 2 - 4\mathrm{i}| \geqslant |z - 2 - 6\mathrm{i}|\)
Argand diagram grid from the Printed Answer Booklet: Re axis from -8 to 8 and Im axis from -8i to 8i, with unit grid squares
[3]
(b) Show that there is a unique value of \(z\), which should be determined, for which both \(|z| \leqslant \sqrt{5}\) and \(|z + 2 - 4\mathrm{i}| \geqslant |z - 2 - 6\mathrm{i}|\). [8]
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