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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

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            

Grade:Upto college level

2 Answers

Aniket Patra
48 Points
10 years ago

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,,

mycroft holmes
272 Points
10 years ago

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 

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