MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade:

                        

If z1, z2, z3 are complex numbers such that |z1|=|z2|=|z3|= | (1/z1) + (1/z2) + (1/z3) | =1 then |z1+z2+z3|=?? How to solve these types of sums??

2 years ago

Answers : (2)

Arun
24737 Points
							
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 
2 years ago
ankit singh
498 Points
							
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
one month ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 101 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details