Region shading with single inequality

Shade a region on an Argand diagram defined by exactly one inequality involving modulus or argument.

2 questions · Moderate -0.6

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CAIE P3 2010 November Q3
6 marks Moderate -0.3
3 The complex number \(w\) is defined by \(w = 2 + \mathrm { i }\).
  1. Showing your working, express \(w ^ { 2 }\) in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real. Find the modulus of \(w ^ { 2 }\).
  2. Shade on an Argand diagram the region whose points represent the complex numbers \(z\) which satisfy $$\left| z - w ^ { 2 } \right| \leqslant \left| w ^ { 2 } \right|$$
OCR MEI FP1 2011 January Q4
6 marks Moderate -0.8
4 Represent on an Argand diagram the region defined by \(2 < | z - ( 3 + 2 \mathrm { j } ) | \leqslant 3\).