Class 11Mathematics1 Complex Numbers and Quadratic Equations: Complex NumbersGeometry of complex numbers
MediumGeometrically,the set $\{z \in \mathbb{C} : |z - 2 - 2i| \leq 1\}$ represents
- Aa closed circular disc with center at $(-2, -2)$ and radius $1$
- Ba closed circular disc with center at $(2, 2)$ and radius $1$
- Ca closed circular disc with center at $(1, 1)$ and radius $0.5$
- Da closed circular disc with center at $(-1, -1)$ and radius $0.5$
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Similar Questions
Match the statements in column-$I$ with those in column-$II$.
[Note: Here $z$ takes the values in the complex plane and $\operatorname{Im} z$ and $\operatorname{Re} z$ denote,respectively,the imaginary part and the real part of $z$]
column-$I$ column-$II$ $(A)$ The set of points $z$ satisfying $|z-i|z||=|z+i|z||$ is contained in or equal to $(p)$ an ellipse with eccentricity $\frac{4}{5}$ $(B)$ The set of points $z$ satisfying $|z+4|+|z-4|=10$ is contained in or equal to $(q)$ the set of points $z$ satisfying $\operatorname{Im} z=0$ $(C)$ If $|\omega|=2$,then the set of points $z=\omega-1/\omega$ is contained in or equal to $(r)$ the set of points $z$ satisfying $|\operatorname{Im} z| \leq 1$ $(D)$ If $|\omega|=1$,then the set of points $z=\omega+1/\omega$ is contained in or equal to $(s)$ the set of points $z$ satisfying $|\operatorname{Re} z| \leq 1$ $(t)$ the set of points $z$ satisfying $|z| \leq 3$
[Note: Here $z$ takes the values in the complex plane and $\operatorname{Im} z$ and $\operatorname{Re} z$ denote,respectively,the imaginary part and the real part of $z$]
| column-$I$ | column-$II$ |
| $(A)$ The set of points $z$ satisfying $|z-i|z||=|z+i|z||$ is contained in or equal to | $(p)$ an ellipse with eccentricity $\frac{4}{5}$ |
| $(B)$ The set of points $z$ satisfying $|z+4|+|z-4|=10$ is contained in or equal to | $(q)$ the set of points $z$ satisfying $\operatorname{Im} z=0$ |
| $(C)$ If $|\omega|=2$,then the set of points $z=\omega-1/\omega$ is contained in or equal to | $(r)$ the set of points $z$ satisfying $|\operatorname{Im} z| \leq 1$ |
| $(D)$ If $|\omega|=1$,then the set of points $z=\omega+1/\omega$ is contained in or equal to | $(s)$ the set of points $z$ satisfying $|\operatorname{Re} z| \leq 1$ |
| $(t)$ the set of points $z$ satisfying $|z| \leq 3$ |
If $z$ and $\omega$ are two non-zero complex numbers such that $|z \omega|=1$ and $\operatorname{Arg}(z) - \operatorname{Arg}(\omega) = \frac{\pi}{2}$,then $\bar{z} \omega =$
If a point $P$ denotes the complex number $z=x+iy$ in the Argand plane and if $\frac{z-(2+i)}{z+(1-2i)}$ is purely real,then the locus of $P$ is
If $|z|=1$ and $z \neq \pm 1$, then all the points representing $\frac{z}{1-z^{2}}$ lie on;
MediumWBJEE 2021
View SolutionLet $A = \{z \in \mathbb{C} : |z - 2| \le 4\}$ and $B = \{z \in \mathbb{C} : |z - 2| + |z + 2| = 5\}$. Then the maximum value of $\{|z_1 - z_2| : z_1 \in A \text{ and } z_2 \in B\}$ is
DifficultJEE MAIN 2026
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