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
prabhav sidhaye Grade: 11
        if Z1 and Z2are 2 complex nos show that they can form an equilatrel triangle with origin if and only if (Z1/Z2 + Z2/Z1)=1
6 years ago

Answers : (2)

SAGAR SINGH - IIT DELHI
879 Points
										

Dear student,


LET A,B,C BE THE VERTICES REPRESENTED BY Z1,Z2,Z3...ABC IS EQUILATERAL HENCE



AB=BC=CA=R SAY............
AB=Z2-Z1...|Z2-Z1|=R
BC=Z3-Z2...|Z3-Z2|=R
CA=Z1-Z3...|Z1-Z3|=R


ANGLES..ABC=BCA=CAB=60 DEG.
ANGLE BETWEEN AB & BC IS ANGLE ABC..THAT IS BETWEEN Z2-Z1 AND Z3-Z2..ETC,..


HENCE IF WE TAKE
AB=Z2-Z1=RE^(iT)............I..........WHERE T IS SOME ANGLE....THEN
BC=Z3-Z2= RE^i(T+60)...........II
CA=Z1-Z3=RE^i(T-60).....................III
SQUARING EQNS.I,II,III AND ADDING
(Z2-Z1)^2+(Z3-Z2)^2+(Z1-Z3)^2=R^2[E^(2iT)+E^2i(T+60)+E^2i(T-60)]
2[Z1^2+Z2^2+Z3^2-Z1Z2-Z2Z3-Z3Z1]=(R^2)(E^2iT)[1+E^(120i)+E^(-120i)]


 


[1+COS(120)+iSIN(120)+COS(-120)+iSIN(-120)]=(R^2)(E^2iT)[1-0.5+iSIN(120)-0.5-iSIN(120)]=0
Z1^2+Z2^2+Z3^2-Z1Z2-Z2Z3-Z3Z1=0
Z1^2+Z2^2+Z3^2=Z1Z2+Z2Z3+Z3Z1



Ultimately it gives (Z1/Z2 + Z2/Z1)=1


 



















Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.


All the best.


Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.


Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..


 


Askiitians Expert


Sagar Singh


B.Tech, IIT Delhi


sagarsingh24.iitd@gmail.com


















6 years ago
mycroft holmes
266 Points
										

6 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details

Ask Experts

Have any Question? Ask Experts

Post Question

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