Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsComplex Number

Paragraph: In argand plane consider A ( z ₁ ), B ( z ₂ ) and C ( z ₃ ) as distinct complex numbers lying on the curve | z ^2 |= 3 . Question: If a root of z₁ z^2+z₂ z+z₃=0 has modulus unity then z₁, z₂, z₃ are in

Options

  1. AA.P.
  2. BG.P.
  3. CH.P.
  4. Dall of above

Correct answer

B. G.P.

Step-by-step solution

Let z_ , z_p be roots of the equation z₁ z^2+z₂ z+z₃=0 such that |z_d |=1 then (z_ +z_ )⁻=z_ z_ ( -z₂ z₁ )⁻= z₃ z₁ z₂^2=z₁ z₃ Hence z₁, z₂, z₃ are in G.P. Since z₁^2+z₂^2+z₃^2=z₁ z₂+z₂ z₃+z₃ z₁ A B C is equilateral. Also PA ^2+ PB ^2+ PC ^2=3 |z₁ |^2- (1+ + ^2 ) z₁^ z - (1+ + ^2 ) z₁ z+ |z₁ |^2+ |z₁ |^2+ |z₁ |^2=6 r^2=18 .

Practice Complex Number on Quantrex Academy →

More from Complex Number

The number of values of z C , satisfying the equations |z-(4+8i)|= 10 and |z-(3+5i)|+|z-(5+11i)|=4 5 , is: 2026Let S = z C : z^2 + 6 ,iz - 3 = 0 . Then _ z S z^8 is equal to : 2026Let the set of all values of k R such that the equation z( z + 2 + i) + k(2 + 3i) = 0 , z C , has at least one solution, be the interval [ , ] . Then 9( + ) is equal to: 2026Let z₁, z₂ C be the distinct solutions of the equation z^2 + 4z - (1 + 12i) = 0 . Then |z₁|^2 + |z₂|^2 is equal to : 2026Let S= z C : z^2+4z+16=0 . Then _ z S |z+ 3 i|^2 is equal to: 2026Let z be a complex number such that |z+2| = |z-2| and ( z+3 z-i ) = 4 . Then |z|^2 is equal to: 2026Let the circles C₁ : |z| = r and C₂ : |z - 3 - 4i| = 5 , z C , be such that C₂ lies within C₁ . If z₁ moves on C₁ , z₂ moves on C₂ and |z₁ - z₂| = 2 , then |z₁ - z₂| is equal to: 2026Let x and y be real numbers such that 50 ( 2x 1+3i - y 1-2i ) = 31 + 17i , i = -1 . Then the value of 10(x - 3y) is : 2026 Full Complex Number list All Most Important Selected Qs for JEE Advanced PYQs