The number of elements in the set {z=a+ib∈C:a,b∈Z,1<∣z−3+2i∣<4} is \_\_\_\_
Answer: 40
Solutions · 1
Official solution
We need lattice points (a,b) with 1<(a−3)2+(b+2)2<16 --- i.e. strictly between a circle of radius 1 and a circle of radius 4, both centred at (3,−2).
Counting all integer lattice points satisfying 1<r2<16 relative to the centre (systematically checking r2=2,4,5,8,9,10,13,16 excluded, etc.) gives a total of 40 lattice points.