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`

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=

z_(1) and z_(2) are the roots of the equaiton z^(2) -az + b=0 where |z_(1)|=|z_(2)|=1 and a,b are nonzero complex numbers, then

If tanx tany=a and x+y=2b show that tanx and tany are the roots of the equation z^2-(1-a)tan2b*z+a=0

If one root of z^2 + (a + i)z+ b +ic =0 is real, where a, b, c in R , then c^2 + b-ac=

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 the complex numbers z_1,z_2,z_3 represents the vertices of a triangle ABC, where z_1,z_2,z_3 are the roots of equation z^3+3alphaz^2+3alphaz^2+3betaz+gamma=0, alpha,beta,gamma beng complex numbers and alpha^2=beta then /_\ABC is (A) equilateral (B) right angled (C) isosceles but not equilateral (D) scalene

Let z_1 and z_2 be theroots of the equation z^2+az+b=0 z being compex. Further, assume that the origin z_1 and z_2 form an equilatrasl triangle then

Number of solutions of Re(z^2)=0 and |z|=rsqrt(2) where z is a complex number and rgt0 is (A) 2 (B) 4 (C) 5 (D) none of these

The roots of the equation z^(4) + az^(3) + (12 + 9i)z^(2) + bz = 0 (where a and b are complex numbers) are the vertices of a square. Then The value of |a-b| is