Random Questions from 2016 Prelims #10

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)

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