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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

Aniket Patra
48 Points
11 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
11 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