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Edexcel A-Level Mathematics A2 Fp2 3 3 Loci and Regions in the Argand Diagram Questions

Practise Edexcel IAL FP2.3.3 by sketching complex loci, converting modulus equations to circles, and using argument conditions to locate intersections.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • convert |z−a| = k|z−b| into a circle and determine its centre and radius
  • use arg(z−a) to form a straight-line condition and locate intersections
  • sketch complex-number loci and regions from modulus or argument conditions

Edexcel A-Level Mathematics A2 Fp2 3 3 Loci and Regions in the Argand Diagram Questions question 1

[Maximum number: 2]

A complex number z is represented by the point P in an Argand diagram.

Given that

|z-2 i|=|z-3|

sketch the locus of P. You do not need to find the coordinates of any intercepts.

The transformation T from the z-plane to the w-plane is given by

w=izz−2iz≠2iw=\frac{\mathrm{i} z}{z-2 \mathrm{i}} \quad z \neq 2 \mathrm{i}

Given that T maps |z-2 i|=|z-3| to a circle C in the w-plane,

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