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

If w=(z)/(z-(1)/(3)i) and |w|=1, then z lies on

Let z and w be non - zero complex numbers such that zw=|z^(2)| and |z-barz|+|w+barw|=4. If w varies, then the perimeter of the locus of z is

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 and w be two complex number such that w = z vecz - 2z + 2, |(z +i)/(z - 3i )|=1 and Re (w) has minimum value . Then the minimum value of n in N for which w ^(n) is real, is equal to "_______."

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 :

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 )