The number of elements in the set z-a+i b ∈ C: a, b ∈ Z and 1

Question

The number of elements in the set z-a+i b ∈ C: a, b ∈ Z and 1 < |z-3+2 i| < 4 is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

1 < |Z-3+2 i| < 4 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/316362e510f5e0f83a4057ddb585abf0-.png" /> 1 < (a-3)2+(b+2)2 < 16 (0, ± 2),(± 2,0),(± 1, ± 2),(± 2, ± 1) (± 2, ± 3),(3 ±, ± 2),(± 1, ± 1),(2 ±, ± 2) (± 3,0),(0, ± 3),(± 3 ± 1),(± 1, ± 3) Total 40 points

Q. The number of elements in the set ${z - a + ib \in C : a, b \in Z$ and $1 < ∣ z - 3 + 2 i ∣ < 4}$ is_____

$1 < ∣ Z - 3 + 2 i ∣ < 4$

$1 < (a - 3)^{2} + (b + 2)^{2} < 16$
$(0, \pm 2), (\pm 2, 0), (\pm 1, \pm 2), (\pm 2, \pm 1)$
$(\pm 2, \pm 3), (3 \pm, \pm 2), (\pm 1, \pm 1), (2 \pm, \pm 2)$
$(\pm 3, 0), (0, \pm 3), (\pm 3 \pm 1), (\pm 1, \pm 3)$
Total $40$ points

Q. The number of elements in the set {z−a+ib∈C:a,b∈Z and 1<∣z−3+2i∣<4} is_____

1<∣Z−3+2i∣<4 1<(a−3)2+(b+2)2<16 (0,±2),(±2,0),(±1,±2),(±2,±1) (±2,±3),(3±,±2),(±1,±1),(2±,±2) (±3,0),(0,±3),(±3±1),(±1,±3) Total 40 points

Q. The number of elements in the set ${z - a + ib \in C : a, b \in Z$ and $1 < ∣ z - 3 + 2 i ∣ < 4}$ is_____

$1 < ∣ Z - 3 + 2 i ∣ < 4$

$1 < (a - 3)^{2} + (b + 2)^{2} < 16$
$(0, \pm 2), (\pm 2, 0), (\pm 1, \pm 2), (\pm 2, \pm 1)$
$(\pm 2, \pm 3), (3 \pm, \pm 2), (\pm 1, \pm 1), (2 \pm, \pm 2)$
$(\pm 3, 0), (0, \pm 3), (\pm 3 \pm 1), (\pm 1, \pm 3)$
Total $40$ points