$\left|\frac{z-1}{z+1}\right|=1$ represents

Important Questions on Complex Numbers

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 2

$\left|z-4\right|<\left|z-2\right|,$ represents the region given by

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 3

If $2z_1-3z_2+z_3=0$ then $z_1,z_2,z_3$ are represented by

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 4

If $z=x+iy$ such that $\left|z+1\right|=\left|z-1\right|$ and $amp\left(\frac{z-1}{z+1}\right)=\frac{\pi }{4}$ then

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 5

If $z^8=\left(z-1\right){}^8,$ then the roots of this equation are

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 6

The equation $z\overline{z}+a\overline{z}+\overline{a}z+b=0,b\in R$ represents a circle, if

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 7

If $z=\left(\lambda +3\right)+i\sqrt{3-{\lambda }^2},$ where $\left|\lambda \right|<\sqrt{3},$ then locus of $z$ is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 8

If a point $P$ denoting the complex number $z$ moves on the complex plane such that $\left|Re\left(z\right)\right|+\left|lm\left(z\right)\right|=1,$ then the locus of $z$ is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Work Book Exercise 4.4>Q 9

The figure formed by four points $1+0i,-1+0i$, $3+4i$ and $\frac{25}{-3-4i}$ on the argand plane is