If all the complex numbers z such that `|z|=1` and `|(z)/(barz)+(barz)/(z)|=1` vertices of a polygon then the area of the polygon is `K` so that `[2K]`, (`[.]` is GIF) equals

If all the complex numbers z such that |z| = 1 and |(z)/(barz)+(barz)/(z)| = 1 are vertices of a polygon then the area of the polygon is K so [2k] is equals ( [.] denotes G.I.F.)

Find the complex number z if z^2+barz =0

Find the complex number z if zbarz = 2 and z + barz=2

Let a be a complex number such that |a| lt 1 and z_(1),z_(2)….. be vertices of a polygon such that z_(k)=1+a+a^(3)+a^(k-1) . Then, the vertices of the polygon lie within a circle.

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

Find all complex numbers satisfying barz = z^2 .

If z is a complex number such that |z - barz| +|z + barz| = 4 then find the area bounded by the locus of z.

If a complex number z satisfies |z|^(2)+(4)/(|z|)^(2)-2((z)/(barz)+(barz)/(z))-16=0 , then the maximum value of |z| is

If omega is any complex number such that z omega = |z|^2 and |z - barz| + |omega + bar(omega)| = 4 then as omega varies, then the area bounded by the locus of z is