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Most Important Selected Qs for JEE AdvancedMathematicsComplex Number

Let a, b, c be distinct complex numbers with |a|=|b|=|c|=1 and z₁, z₂ be the roots of the equation a z^2+b z+c=0 with |z₁ |=1 . Also P and Q are the points representing the complex numbers z₁ and z₂ respectively in the complex plane with P O Q= (where O being the origin) then which of the following is/are correct?

Options

  1. Ab^2=a c
  2. B= 2 3
  3. CP Q= 3
  4. D|z₁+z₂ |=1

Correct answer

D. |z₁+z₂ |=1

Step-by-step solution

aligned & |z₁ z₂ |= | c a |=1, & |z₁+z₂ |= | -b a |=1 & (z₁+z₂ ) ( z ₁+ z ₂ )=1 (z₁+z₂ ) ( 1 z₂ + 1 z₂ )=1 & (z₁+z₂ )^2=z₁ z₂ & aligned aligned & ( -b a )^2= c a b^2=a c & |z₁+z₂ |= |z₁ | |1+e^ i |=2 2 =1 = 2 3 & P Q= |z₂-z₁ |= |z₁ | |e^ i -1 |=2 2 &=2 3 = 3 aligned

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