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

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

Complex numbers z_1 , z_2 , z_3 are the vertices A, B, C respectively of an isosceles right angled trianglewith right angle at C and (z_1- z_2)^2 = k(z_1 - z_3) (z_3 -z_2) , then find k.

Complex numbers z_1 , z_2 , z_3 are the vertices A, B, C respectively of an isosceles right angled trianglewith right angle at C and (z_1- z_2)^2 = k(z_1 - z_3) (z_3 -z_2) , then find k.

If z_1 , z_2 ,z_3 are the vertices of an isosceles triangle right angled at z_2 , then prove that (z_1)^2+2(z_2)^2+(z_3)^2=2(z1+z3)z2

z_1, z_2 and z_3 are the vertices of an isosceles triangle in anticlockwise direction with origin as in center , then prove that z_2, z_1 and kz_3 are in G.P. where k in R^+dot

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

If z_1,z_2,z_3 be the vertices A,B,C respectively of triangle ABC such that |z_1|=|z_2|=|z_3| and |z_1+z_2|=|z_1-z_2| then C= (A) pi/2 (B) pi/3 (C) pi/6 (D) pi/4