Let `A` and `B` represent `z_(1)` and `z_(2)` in the Argand plane and `z_(1),z_(2)` be the roots of the equation `Z^(2)+pZ+q=0` ,where `p, q` are complex numbers. If `O` is the origin, `OA=OB` and `/_AOB=alpha` then `p^(2)=`

If p represent z=x+iy in the argand plane and |z-1|^(2)+|z+1|^(2)=4 then the locus of p is

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 z_(1) and z_(2) are the roots of the equation az^(2)+bz+c=0,a,b,c in complex number and origin z_(1) and z_(2) form an equilateral triangle,then find the value of (b^(2))/(ac) .

Let a , b , c be distinct complex numbers with |a|=|b|=|c|=1 and z_(1) , z_(2) be the roots of the equation az^(2)+bz+c=0 with |z_(1)|=1 . Let P and Q represent the complex numbers z_(1) and z_(2) in the Argand plane with /_POQ=theta , o^(@) lt 180^(@) (where O being the origin).Then

On the Argand plane ,let z_(1) = - 2+ 3z,z_(2)= - 2-3z and |z| = 1 . Then

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=x+iy and if the point p in the argand plane represents z ,then the locus of z satisfying Im (z^(2))=4