Quick questions on Loci in the Argand diagram explained: H2 Further Mathematics

The key idea is that $|z - a|$ is the distance from the point $z$ to the fixed point $a$ on the Argand diagram. Every locus in this topic is built from this reading.

is the set of points at distance $r$ from $a$, a circle of radius $r$ centred at the point $a$. The inequality $|z - a| \leq r$ shades the closed disc, and $|z - a| > r$ the exterior.

is the set of points equidistant from $a$ and $b$, the perpendicular bisector of the segment joining them. The inequality $|z - a| < |z - b|$ shades the half-plane nearer to $a$.

is a half-line (ray) starting from the point $a$ (excluded) and making angle $\theta$ with the positive real direction. It is a ray, not a full line, because the argument fixes the direction. A range $\alpha \leq \arg(z - a) \leq \beta$ shades the sector between two rays from $a$.

$|z - a| = r$ is centred at $+a$; for $|z + 3 - 2i|$ rewrite as $|z - (-3 + 2i)|$ so the centre is $(-3, 2)$.

Describe the locus $|z - 5| = 3$. [1 mark]

What locus is given by $|z - 2| = |z - 6|$? [1 mark]

Describe $\arg(z - i) = \dfrac{\pi}{2}$. [2 marks]