Thank you for registering.

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

Please check your email for login details.
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 A(Z 1),B(Z2),C(Z3) on complex plane such that angles at B and C are each equal to 1/2(∏-α) then prove that (Z2-Z3) 2 =4(Z3 - Z1)(Z1-Z2)sin 2 α/2

if A(Z1),B(Z2),C(Z3) on complex plane such that angles at B and C are each equal to 1/2(∏-α) then prove that (Z2-Z3)2 =4(Z3 - Z1)(Z1-Z2)sin2 α/2

Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear deepika


<B =<c =(∏-α)/2    so angel A = α

now use sine rule in trinagle ABC

|z2 -z3|/sinα  = |z1-z3|/cosα = |z1-z2|/cosα

now by the rotation property of vector

(z2-z3)/|z2 -z3|  = (z1-z3)/|z1-z3|  ei(∏-α)/2   ...........1


and  also (z2-z3)/|z2 -z3| = (z2-z1)/|z2-z1|  ei(∏-α)/2   ...........2


multiple first and second equation

(Z2-Z3)2  /|z2 -z3|2=(Z3 - Z1)(Z1-Z2)/|z1-z3||z2-z1|


now put the value of |z1-z3|, |z2-z1| in terms of |z2 -z3|

(Z2-Z3)2  =sin2α(Z3 - Z1)(Z1-Z2)/cos2α/2

(Z2-Z3)2 =4sin2α/2 (Z3 - Z1)(Z1-Z2)

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.
 
Regards,
Askiitians Experts
Badiuddin



Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free