0

ADNAN MUHAMMED

Grade 12,

Courses New

i want solution of question number 21. Please also give me a easy trick for solving this question in jee if exists.

i want solution of question number 21. Please also give me a easy trick for solving this question in jee if exists.

Question Image
Grade:11

1 Answers

Vikas TU
14149 Points
3 years ago
Dear student 
Given : | z₁ | = | z₂ | = | z₃ | = 1 ............. (1) 
. . . . . . | 1/z₁ + 1/z₂ + 1/z₃ | = 1 ............ (2) 
__________________________ 
To Find : | z₁ + z₂ + z₃ |. 
__________________________ 
We note that 
(i) | z | = | z' |, ... z' is conjugate of z 
(ii) z·z' = | z |² = | z' |² 
(iii) Σ(z') = [ Σ(z) ]'. 
__________________________ 
If | z | = 1, then : z·z' = 1, i.e., (1/z) = z'...... (3) 
∴ | z₁ + z₂ + z₃ | 
= | ( z₁ + z₂ + z₃ )' | 
= | (z₁)' + (z₂)' + (z₃)' | 
= | 1/z₁ + 1/z₂ + 1/z₃ | ........ from (3) 
= 1 ...................................... from (2) 
__________________ 
∴ | z₁ + z₂ + z₃ | = 1 
 

Think You Can Provide A Better Answer ?

Other Related Questions on Mechanics

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More