OCR Further Pure Core 1 2024 June — Question 2

Exam BoardOCR
ModuleFurther Pure Core 1 (Further Pure Core 1)
Year2024
SessionJune
TopicComplex Numbers Argand & Loci

2 The locus \(C _ { 1 }\) is defined by \(C _ { 1 } = \left\{ z : 0 \leqslant \arg ( z + i ) \leqslant \frac { 1 } { 4 } \pi \right\}\).
  1. Indicate by shading on the Argand diagram in the Printed Answer Booklet the region representing \(C _ { 1 }\).
  2. Determine whether the complex number \(1.2 + 0.8\) is is \(C _ { 1 }\). The locus \(C _ { 2 }\) is the set of complex numbers represented by the interior of the circle with radius 2 and centre 3 . The locus \(C _ { 2 }\) is illustrated on the Argand diagram below.
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  3. Use set notation to define \(C _ { 2 }\).
  4. Determine whether the complex number \(1.2 + 0.8\) is in \(C _ { 2 }\).