If $w = \frac{z}{z - \frac{1}{3}i}$ and $|w| = 1$,where $i = \sqrt{-1}$,then $z$ lies on

If $z=x+iy$,then the equation $|z+1|=|z-1|$ represents

If $z = \sqrt{2} - i\sqrt{2}$ is rotated through an angle $45^{\circ}$ in the anti-clockwise direction about the origin,then the coordinates of its new position are

The locus of the point $z=x+iy$ satisfying $\left|\frac{z-2i}{z+2i}\right|=1$ is

The locus of the points represented by $|z+3|-|z-3|=6$,where $z$ is a complex number,is ....

If for the complex numbers $z$ satisfying $|z-2-2 i| \leq 1$,the maximum value of $|3 i z+6|$ is attained at $a+i b$,then $a+b$ is equal to .... .