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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 let P and Q represents the complex numbers z₁ and z ₂ in the complex plane with POQ = where O is the origin then

Options

  1. Ab ^2= ac , = 2 3
  2. B= 2 3 , P Q= 3
  3. Cb^2=a c, P Q=2 3
  4. D2 b^2=a c, = 3

Correct answer

B. = 2 3 , P Q= 3

Step-by-step solution

aligned & |z₁ |= |z₂ |=1 ; |z₁+z₂ |=1 & (z₁+z₂ ) ( z ₁+ z ₂ )=1 aligned aligned & |z₁+z₂ |= |z₁ | |1+e^ i |=1 & |z₂-z₁ |= |z₁ | |e^ i -1 | aligned

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