All flashcards topics

Loci in the Argand diagramAQA A-Level Further Maths: Flashcards

What these 12 flashcards ask

  • What does |z-a| represent?
  • Locus of |z-a|=r?
  • Cartesian form of |z-(a+bi)|=r?
  • Region |z-a|r?
  • Locus of |z-a|=|z-b|?
  • Locus of \arg(z-a)=\theta?
  • Cartesian form of \arg(z-(a+bi))=\theta?
  • Centre of |z+1-2i|=4?
  • Region \alpha<\arg(z-a)<\beta?
  • Why is a itself excluded from \arg(z-a)=\theta?
  • Greatest |z| on |z-a|=r?
  • Sector and segment area (radians)?

Exam questions on Loci in the Argand diagram

  1. The complex number zz satisfies ∣z−3+4i∣=5|z-3+4\mathrm{i}|=5.
    Find the Cartesian equation of the locus of zz.2 marks
  2. The complex number zz satisfies arg⁡(z+2−i)=π4\arg(z+2-\mathrm{i})=\frac{\pi}{4}.
    Find the Cartesian equation of the locus of zz, stating any restriction on xx.2 marks
  3. The complex number zz satisfies ∣z−2∣=∣z−2i∣|z-2|=|z-2\mathrm{i}|.
    Find the Cartesian equation of the locus of zz.3 marks
See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).