Click to Chat

1800-2000-838

+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
Menu
rachneet kaur Grade:
`        if ABC is an equilateral triangle then if A and B are denoted by complex nos z1 and z2 then prove that C is denoted by z3 =z1 e^-i(pi\3)+z2 e^i(pi\3).`
7 years ago

## Answers : (1)

Priyansh Bajaj AskiitiansExpert-IITD
30 Points
```
Dear Rachneet Kaur,
Solution:- By rotation theorem of complex no.'s, ((z3 - z1) / (z2 - z1)) = ( |z3 - z1| / |z2 - z1| )e^i(pi/3)
[Refer Rotation Theorem from http://www.askiitians.com/iit-jee-algebra/complex-numbers/rotation.aspx ]
Since ABC is an equilateral triangle, |z3 - z1| = |z2 - z1|
So, we get ((z3 - z1) / (z2 - z1)) = e^i(pi/3)
or, (z3 - z1) = e^i(pi/3) (z2 - z1)
or, z3 = z2 e^i(pi/3) + z1 (1-e^i(pi/3))

or, z3 = z2 e^i(pi/3) + z1 (1/2 - i (sqrt(3)/2))

or, z3 = z2 e^i(pi/3) + z1 e^-i(pi/3)

Hence Proved.
Please feel free to post as many doubts on our discussion forum as  you can. If you find any question Difficult to understand - post it  here and we will get you the answer and detailed solution very quickly.  We are all IITians and here to help you in your IIT JEE preparation.
All the best Rachneet Kaur!!!
Regards,
Askiitians Experts
Priyansh Bajaj

```
7 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

## Other Related Questions on Algebra

View all Questions »
• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: Rs. 15,900
• View Details
Get extra Rs. 1,272 off
USE CODE: Neerajwin
Get extra Rs. 187 off
USE CODE: Neerajwin

## Ask Experts

Have any Question? Ask Experts

Post Question

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