Most Important Selected Qs for JEE AdvancedMathematicsComplex Number
Paragraph Consider a circle centred at origin O and passing through points A ( z ₁ ), B ( z ₂ ) and C ( z ₃ ) . The tangents to the circle at A , B and C intersect at D , E and F ; D , E , F are opposite to A , B , C respectively. Also AOB = BOC = , where ( 2 , ) satisfying the equation 17 ^2 x+16 ( 1 2 x x-1 ) =-2 x(1+4 x) On the basis of above information, answer the following : Question The complex representation
Options
- Az ₁+ z ₂ 2
- Bz ₁ z ₂
- C2 z ₁ z ₂ z ₁+ z ₂
- Dz ₁+ Z ₂ Z ₁ Z ₂
Correct answer
C. 2 z ₁ z ₂ z ₁+ z ₂
Step-by-step solution
Let |z₁ |= |z₂ |= |z₃ |=a If z be the complex representation of F , then z-z₁ z₁ + z - z ₁ z ₁ =0 i.e., z ₁ z+ z z₁=2 a^2...(i) similarly, z ₂ z+ z z₂=2 a^2 ....(ii) From (i) and (ii), we have ( z ₁ z₂- z ₂ z₁ ) z=2 a^2 (z₂-z₁ ) a ^2 ( z ₂ z ₁ - z ₁ z ₂ ) z =2 a ^2 ( z ₂- z ₁ ) or z = 2 z ₁ z ₂ z₁+ z ₂