If `w` is a complex number such that `|w|=r!=1,Z=w+(1)/(w)` describes a conic,then distance between foci is

Let Z and w be two complex number such that |zw|=1 and arg(z)-arg(w)=pi/2 then

If z and w are two complex number such that |zw|=1 and arg(z)arg(w)=(pi)/(2), then show that bar(z)w=-i

Let z=x+iy and w=u+iv be two complex numbers, such that |z|=|w|=1 and z^(2)+w^(2)=1. Then, the number of ordered pairs (z, w) is equal to (where, x, y, u, v in R and i^(2)=-1 )

Let a complex number be w=1-sqrt3 I, Let another complex number z be such that |z w|=1 and arg(z)-arg (w) =pi/2 . Then the area of the triangle with vertices origin, z and w is equal to :

If z and w are two non - zero complex numbers such that |zw|=1 and arg(z)-arg(w)=(pi)/(2), then the value of 5ibarzw is equal to

If complex variables z,w are such that w=(2z-7i)/(z+i) and |w|=2, then z lies on:

Let z and omega be complex numbers such that |z|=|omega| and arg (z) dentoe the principal of z. Statement-1: If argz+ arg omega=pi , then z=-baromega Statement -2: |z|=|omega| implies arg z-arg baromega=pi , then z=-baromega

Let z and w be two complex numbers such that |Z|<=1,|w|<=1 and |z+iw|=|z-ibar(w)|=2