Loci and regions in the Argand diagram

Loci and regions in the Argand diagram Quiz

Spec 3.3 · Edexcel International A Level Further Maths: Quiz

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  1. 1. The locus ∣z−1+2i∣=3|z-1+2i|=3 is a circle with

    • A. centre −1+2i-1+2i, radius 33
    • B. centre 1+2i1+2i, radius 33
    • C. centre 1−2i1-2i, radius 33
    • D. centre 1−2i1-2i, radius 99

  2. 2. The Cartesian equation of arg⁡(z−2i)=π4\arg(z-2i)=\frac\pi4 is

    • A. y=x−2, x>0y=x-2,\ x>0
    • B. y=x+2, x>0y=x+2,\ x>0
    • C. y=−x+2, x>0y=-x+2,\ x>0
    • D. y=x+2, x<0y=x+2,\ x<0

  3. 3. The locus of ∣z∣=∣z−4∣|z|=|z-4| is

    • A. the circle ∣z∣=2|z|=2
    • B. the line y=2y=2
    • C. the line x=4x=4
    • D. the line x=2x=2

  4. 4. The region ∣z−1∣≤2|z-1|\le2 is

    • A. the closed disc centre 11, radius 22
    • B. the exterior of the circle
    • C. the circle only
    • D. a half-plane

  5. 5. The locus ∣z−a∣=k∣z−b∣|z-a|=k|z-b| with k≠1k\neq1 is

    • A. a straight line
    • B. a half-line
    • C. a circle
    • D. an ellipse

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