(A) Let $z = x + iy$. Substituting this into the equation: $|(x+1) + i(y-1)| = |(x-1) + i(y+1)|$. Squaring both sides: $(x+1)^2 + (y-1)^2 = (x-1)^2 +

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

Straight line passing through the origin and the first and third quadrant.

(A) Let $z = x + iy$. Substituting this into the equation: $|(x+1) + i(y-1)| = |(x-1) + i(y+1)|$. Squaring both sides: $(x+1)^2 + (y-1)^2 = (x-1)^2 + (y+1)^2$. Expanding the terms: $x^2 + 2x + 1 + y^2 - 2y + 1 = x^2 - 2x + 1 + y^2 + 2y + 1$. Simplifying: $2x - 2y = -2x + 2y$. $4x = 4y$,which implies $y = x$. The equation $y = x$ represents a straight line passing through the origin and the first and third quadrants.

Class 11 Mathematics 4-1.Complex numbers Geometry of complex numbers

Easy

The equation $|z+1-i|=|z-1+i|$ represents a (where $z$ is a complex number)

MHT CET 2025 All MHT CET

A
Straight line passing through the origin and the first and third quadrant.
B
Straight line passing through the origin and the second and fourth quadrant.
C
Straight line passing through the point $(1, -1)$ and having slope $-1$.
D
Straight line passing through the point $(2, 1)$ and having slope $\frac{1}{2}$.

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

4-1.Complex numbers

Subtopic

Geometry of complex numbers

Previous Year

MHT CET 2025 Paper All MHT CET years →

What are the polar coordinates of the point $(-\sqrt{3}, 1)$?

Easy

View Solution

The locus of the complex number $z$ such that $\arg \left(\frac{z-2}{z+2}\right)=\frac{\pi}{3}$ is:

DifficultAP EAMCET 2011

View Solution

If $\cos \alpha + 2 \cos \beta + 3 \cos \gamma = 0$,$\sin \alpha + 2 \sin \beta + 3 \sin \gamma = 0$ and $\alpha + \beta + \gamma = \pi$,then $\sin 3 \alpha + 8 \sin 3 \beta + 27 \sin 3 \gamma$ is equal to

MediumKCET 2012

View Solution

In the Argand plane,the distinct roots of $1+z+z^{3}+z^{4}=0$ ($z$ is a complex number) represent vertices of

MediumWBJEE 2014

View Solution

If $\left| z - \frac{1 + 3i}{2} \right| = \frac{\sqrt{10}}{2}$ and $P$,$Q$,and $R$ are points representing the complex numbers $z$,$z e^{i \pi / 3}$,and $z(1 + e^{i \pi / 3})$ respectively in the Argand plane,then the area of the triangle $PQR$ is:

EasyAP EAMCET 2019

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The equation $|z+1-i|=|z-1+i|$ represents a (where $z$ is a complex number)

Similar Questions

What are the polar coordinates of the point $(-\sqrt{3}, 1)$?

The locus of the complex number $z$ such that $\arg \left(\frac{z-2}{z+2}\right)=\frac{\pi}{3}$ is:

If $\cos \alpha + 2 \cos \beta + 3 \cos \gamma = 0$,$\sin \alpha + 2 \sin \beta + 3 \sin \gamma = 0$ and $\alpha + \beta + \gamma = \pi$,then $\sin 3 \alpha + 8 \sin 3 \beta + 27 \sin 3 \gamma$ is equal to

In the Argand plane,the distinct roots of $1+z+z^{3}+z^{4}=0$ ($z$ is a complex number) represent vertices of

If $\left| z - \frac{1 + 3i}{2} \right| = \frac{\sqrt{10}}{2}$ and $P$,$Q$,and $R$ are points representing the complex numbers $z$,$z e^{i \pi / 3}$,and $z(1 + e^{i \pi / 3})$ respectively in the Argand plane,then the area of the triangle $PQR$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module