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Edexcel IAL Mathematics FP2.3.3 Argand loci and regions

Practise interpreting modulus and argument conditions as Argand loci, then finding intersections, centres, radii, or represented points.

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

FP2.3.3 - Loci and regions in the Argand diagram 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=izz2iz2iw=\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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