Loci in the Argand diagram Quiz

1. What is the centre of the circle $|z-2+3\mathrm{i}|=4$?

• A. $-2+3\mathrm{i}$
• B. $2+3\mathrm{i}$
• C. $2-3\mathrm{i}$
• D. $3-2\mathrm{i}$

2. Which describes $|z-1|\ge2$?

• A. On or outside the circle with centre $1$ and radius $2$
• B. Inside the circle with centre $1$ and radius $2$
• C. On or outside the circle with centre $-1$ and radius $2$
• D. On or outside the circle with centre $1$ and radius $4$

3. What is the locus of $|z-1|=|z+1|$?

• A. The real axis
• B. The circle $|z|=1$
• C. The line $y=1$
• D. The imaginary axis

4. Describe $\arg(z-1)=\frac{\pi}{2}$.

• A. The line $x=1$ for $y<0$
• B. The imaginary axis
• C. The half-line $x=1$, $y>0$
• D. The half-line $y=1$, $x>0$

5. Which point lies on $\arg(z-\mathrm{i})=\frac{3\pi}{4}$?

• A. $1+2\mathrm{i}$
• B. $-1+2\mathrm{i}$
• C. $-1$
• D. $1$