Let `z_1,z_2 ` and origin be the vertices A,B,O respectively of an isosceles triangle OAB, where OA=OB and `/_AOB=2theta. If z_1, z_2` are the roots of equation `z^2+z+9=0` then `sec^2theta=`

Let z_1,z_2 and origin represent vertices A,B,O respectively of an isosceles triangel OAB, where OA=OB and /_AOB=2theta. If z_1,z_2 are the roots of the equation z^2+2az+b=0 where a,b re comlex numbers then cos^2theta= (A) a/b (B) a^2/b^2 (C) a/b^2 (D) a^2/b

If z_(1),z_(2) are roots of equation z^(2)-az+a^(2)=0 then |(z_(1))/(z_(2))|=

In an Agrad plane z_(1),z_(2) and z_(3) are, respectively, the vertices of an isosceles trinagle ABC with AC= BC and /_CAB = theta . If z_(4) is incentre of triangle, then The value of (z_(2)-z_(1))^(2)tan theta tan theta //2 is

In an Agrad plane z_(1),z_(2) and z_(3) are, respectively, the vertices of an isosceles trinagle ABC with AC= BC and /_CAB = theta . If z_(4) is incentre of triangle, then The value of (z_(4) -z_(1))^(2) (cos theta + 1) sec theta is

In an Agrad plane z_(1),z_(2) and z_(3) are, respectively, the vertices of an isosceles trinagle ABC with AC= BC and /_CAB = theta . If z_(4) is incentre of triangle, then The value of AB xx AC// (IA)^(2) is

On the Argand plane z_(1),z_(2) and z_(3) are respectively,the vertices of an isosceles triangle ABC with AC=BC and equal angles are theta. If z_(4) is the incenter of the triangle,then prove that (z_(2)-z_(1))(z_(3)-z_(1))=(1+sec theta)(z_(4)-z_(1))^(2)

Complex numbers z_1 , z_2, z_3 are the vertices A, B, C respectively of an isosceles right angled triangle with right angle at C. Show that (z_1-z_2)^2 =2 (z_1 - z_3) (z_3-z_2) .

Let the complex numbers Z_(1), Z_(2) and Z_(3) are the vertices A, B and C respectively of an isosceles right - angled triangle ABC with right angle at C, then the value of ((Z_(1)-Z_(2))^(2))/((Z_(1)-Z_(3))(Z_(3)-Z_(2))) is equal to