If `w=z//[z-(1//3)i]a n d|w|=1,` then find the locus of `zdot`

If w=z/[z-(1/3)i] and |w|=1, then find the locus of z

If omega = z//[z-(1//3)i] and |omega| = 1 , then find the locus of z.

If |z-5i|=|z+5i| , then the locus of zdot

If z = x + yi, omega = (2-iz)/(2z-i) and |omega|=1 , find the locus of z in the complex plane

If complex number z lies on the curve |z - (- 1+ i)| = 1 , then find the locus of the complex number w =(z+i)/(1-i), i =sqrt-1 .

If the equation |z-a|+|z-b|=3 represents an ellipse and a ,b in C ,w h e r ea is fixed, then find the locus of bdot

If z is any complex number such that |3z-2|+|3z+2|=4 , then identify the locus of zdot

If [x y4z+6x+y]=[8w0 6] , then find the values of x ,\ y ,\ z\ a n d\ w .

If z=x+i y and w=(1-i z)//(z-i) and |w| = 1 , then show that z is purely real.

If |z|=1 and let omega=((1-z)^2)/(1-z^2) , then prove that the locus of omega is equivalent to |z-2|=|z+2|