Further loci and regions in the Argand diagram

Further loci and regions in the Argand diagram Quiz

Spec 4.1 · Edexcel A-Level Further Maths: Quiz

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5 questions, one answer each

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1. The locus $|z-2|=|z+2i|$ has Cartesian equation
- A. $y=x$
- B. $y=-x$
- C. $x=2$
- D. $x^2+y^2=4$
2. The locus $|z|=2|z-3|$ is a circle with
- A. centre $3$ , radius $2$
- B. centre $6$ , radius $2$
- C. centre $4$ , radius $2$
- D. centre $4$ , radius $4$
3. $\arg\left(\frac{z-1}{z+1}\right)=\frac{\pi}{2}$ is
- A. a straight line
- B. the whole circle $|z|=1$
- C. the lower semicircle of $|z|=1$
- D. the upper semicircle of $|z|=1$
4. The region $1\leq\mathrm{Re}(z)\leq3$ is
- A. a vertical strip
- B. a horizontal strip
- C. an annulus
- D. a wedge
5. The region $0\leq\arg(z-1)\leq\frac{\pi}{2}$ is
- A. the first quadrant
- B. the quarter-plane $x\geq1$ , $y\geq0$
- C. the half-plane $x\geq1$
- D. a quarter-disc