Class 11Mathematics1 Complex Numbers and Quadratic Equations: Complex NumbersGeometry of complex numbers
DifficultThe locus of $z$ which lies in the shaded region is best represented by
- A$z: |z + 1| > 2, |\arg(z + 1)| < \pi/4$
- B$z: |z - 1| > 2, |\arg(z - 1)| < \pi/4$
- C$z: |z + 1| < 2, |\arg(z + 1)| < \pi/2$
- D$z: |z - 1| < 2, |\arg(z - 1)| < \pi/2$
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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 $|z| \leq 3$ |
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