Browse by Stream
Discuss Doubts
Home
Search for Exam, Articles, Questions
get app
Go To Your Study Dashboard
  1. Home
  2. Can someone explain - Complex numbers and quadratic equations - JEE Main-10
# Engineering

All the points in the set 

S=\left \{ \frac{\alpha +i}{\alpha -i}:\alpha\; \epsilon\; \mathbf{R} \right \}\left ( i=\sqrt{-1} \right )  lie on a :

  • Option 1)

    straight line whose slope is 1.

  • Option 2)

    circle whose radius is 1.

  • Option 3)

    circle whose radius is \sqrt{2} .

  • Option 4)

    straight line whose slop is -1

 

Answers (1)
S solutionqc

Given , S= \frac{\alpha +i}{\alpha -i}:\alpha\; \epsilon\; \mathbf{R}

  S=x+iy

x+iy=\frac{\left ( \alpha +i \right )^{2}}{\alpha ^{2}+1}=\frac{\alpha ^{2}-1+2\alpha i}{\alpha ^{2}+1}

x=\frac{\alpha ^{2}-1}{\alpha +1}=y=\frac{2\alpha}{\alpha ^{2}+1}

x^{2}+y^{2}=\frac{\left ( \alpha ^{2}-1^{2} \right )+4\alpha ^{2}}{\left ( \alpha ^{2}+1 \right )^{2}}=1

x^{2}+y^{2}=1


Option 1)

straight line whose slope is 1.

Option 2)

circle whose radius is 1.

Option 3)

circle whose radius is \sqrt{2} .

Option 4)

straight line whose slop is -1

Similar Questions

Preparation Products

Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Test Series JEE Main April 2021

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 6999/- ₹ 4999/-
Buy Now
JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Test Series JEE Main April 2022

Take chapter-wise, subject-wise and Complete syllabus mock tests and get an in-depth analysis of your test..

₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
Start Now
 
Exams
Articles
Questions