PJC P2 Q1

The complex numbers a and b are given by $2 + 3i$ and $-4-5i$ respectively.

(i) On a single Argand diagram, sketch the loci
(a) $|2z-a-b| = |a-b|$
(b) $0 \le \text{arg}(z-b) \le \text{arg}(a - b)$

(ii) Find the range of $\text{arg}(z)$ where $z$ is the complex number that satisfies the relationships in part (i)