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-3i|=|z+3i| , then find the locus of z.

If a gt 0 and the equation |z-a^(2)|+|z-2a|=3 , represents an ellipse, then 'a' belongs to the interval

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

Let z_1 and z_2 be the roots of the equation 3z^2 + 3z + b=0 . If the origin, together with the points represented by z_1 and z_2 form an equilateral triangle then find the value of b.

If Im((z-1)/(e^(theta i))+(e^(theta i))/(z-1))=0, then find the locus of z

Variable complex number z satisfies the equation |z-1+2i|+|z+3-i|=10 . Prove that locus of complex number z is ellipse. Also, find the centre, foci and eccentricity of the ellipse.

The equation zbar(z)+abar(z)+bar(a)z+b=0,b in R represents circle,if

The largest value of r for which the region represented by the set {omega in C/| omega-4-i|<=r} is contained in the region represented by the set {z in C/|z-1|<=|z+i|}, is equal to