The number of elements in the set { z = a + i | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given condition is $1 < |z - (3 - 2i)| < 4$. Let $z = a + ib$,where $a, b \in \mathbb{Z}$.This represents the region between two circles cente

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(A) The given condition is $1 This represents the region between two circles centered at $(3, -2)$ with radii $r_1 = 1$ and $r_2 = 4$.The inequality is $1 Let $x = a - 3$ and $y = b + 2$. Since $a, b \in \mathbb{Z}$,$x, y \in \mathbb{Z}$.We need to find the number of integer pairs $(x, y)$ such that $1 Possible values for $x^2 + y^2$ are $2, 4, 5, 8, 9, 10, 13$.- For $x^2 + y^2 = 2$: $(\pm 1, \pm 1)$ $\rightarrow 4$ points.- For $x^2 + y^2 = 4$: $(\pm 2, 0), (0, \pm 2)$ $\rightarrow 4$ points.- For $x^2 + y^2 = 5$: $(\pm 1, \pm 2), (\pm 2, \pm 1)$ $\rightarrow 8$ points.- For $x^2 + y^2 = 8$: $(\pm 2, \pm 2)$ $\rightarrow 4$ points.- For $x^2 + y^2 = 9$: $(\pm 3, 0), (0, \pm 3)$ $\rightarrow 4$ points.- For $x^2 + y^2 = 10$: $(\pm 1, \pm 3), (\pm 3, \pm 1)$ $\rightarrow 8$ points.- For $x^2 + y^2 = 13$: $(\pm 2, \pm 3), (\pm 3, \pm 2)$ $\rightarrow 8$ points.Total number of points = $4 + 4 + 8 + 4 + 4 + 8 + 8 = 40$.

The number of elements in the set $\{ z = a + ib \in \mathbb{C} : a, b \in \mathbb{Z} \text{ and } 1 < |z - 3 + 2i| < 4 \}$ is:

Similar Questions

If $A = \{z = x + iy : \text{real part of } \frac{\bar{z}-1}{z-i} = 2\}$,then the locus of the point $P(x, y)$ in the Cartesian plane is:

The locus of the point $z=x+iy$ satisfying the equation $\left|\frac{z-1}{z+1}\right|=1$ is given by :

The vertices $B$ and $D$ of a parallelogram are $1 - 2i$ and $4 + 2i$. If the diagonals are at right angles and $AC = 2BD$,the complex number representing $A$ is

$A$ complex number $z$ is said to be unimodular if $|z| = 1$. Suppose $z_1$ and $z_2$ are complex numbers such that $\frac{z_1 - 2z_2}{2 - z_1 \overline{z_2}}$ is unimodular and $z_2$ is not unimodular. Then the point $z_1$ lies on a:

Let $z \in \mathbb{C}$ be a complex number. The equation $2|z + 3i| - |z - i| = 0$ represents:

Vedclass Test Series

Exam Paper Generator

Online Exam Module