×

#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

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
```
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??
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

Arun
25768 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
609 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
```
5 months ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Algebra

View all Questions »

### 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