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sachin yadav Grade: Upto college level
        

let p and q be complex numbers with |a|=|b|=|c|.  (A) prove that if a root of the eqauation azsqaur+bz+c=0 has modulas equal to 1,then bsquar=ac            

6 years ago

Answers : (2)

Aniket Patra
48 Points
										

Since the modulus of one of the root is 1,it satisfies the condition for reality i.e. b^2 - 4ac > 0..which gives ur answer,,

6 years ago
mycroft holmes
266 Points
										

We will repeatedly invoke the result that if |z| =1 then 


 


We have here three complex numbers with modulus 1,  where  is the root of the equation.


 


So, we have  ........................1 which can be written as 


 


Taking conjugates on both sides and using the result mentioned above, we have 


 


 which translates to ........................2


 


Multiplying 1 by b, we get .....................3


 


Subtracting 2 and 3, we get 

6 years ago
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