Im
3
2
1
-5 -4 -3 -2 -1 0 1 Re
-1
Figure 1
Figure 1 shows an Argand diagram.
The set P, of points that lie within the shaded region including its boundaries, is defined by
where a, b, c and d are integers.
P = \{z \in C: a < |z + b + ci| \le d\}
(a) Write down the values of a, b, c and d.
The set Q is defined by
Q = \{z \in C: a \le |z+b+ci| < d\} \cap \{z \in C : |z-i| < |z-3i|\}
(b) Determine the exact area of the region defined by Q, giving your answer in
simplest form.
(3)
(7)
