Find the minimum value of the expression `E= |z|^2+ |z-3|^2 + |z- 6i|^2` (where `z=x+iy, x,y in R`)

Find the minimum value of |z-1 if ||z-3|-|z+1||=2.

Find the locus of z if |3z - 5 | = 3 |z + 1| where z = x + iy

For any complex number z find the minimum value of |z|+|z-2i|

If z=x+iy (x, y in R, x !=-1/2) , the number of values of z satisfying |z|^n=z^2|z|^(n-2)+z |z|^(n-2)+1. (n in N, n>1) is

If z is a complex number, then find the minimum value of |z|+|z-1|+|2z-3|dot

Find all the possible values of following expressions : (i) ( |x|)/(x) + (|y|)/y (ii) |x|/x+|y|/y+|z|/z

Find the equation of the plane through the intersection of the planes 2x - 3y + z - = 0 and x - y + z + 1 = 0 and perpendicular to the plane x + 2y - 3z + 6 = 0.