1. If `|z-2+i| ≤`2 then find the greatest and least value of` | z| `

If |z-4/z|=2 then the greatest value of |z| is:

If |z_(1) -1|le,|z_(2) -2| le2,|z_(3) - 3|le 3, then find the greatest value of |z_(1) + z_(2) + z_(3)|

For any two complex numbers z_(1) "and" z_(2) , abs(z_(1)-z_(2)) ge {{:(abs(z_(1))-abs(z_(2))),(abs(z_(2))-abs(z_(1))):} and equality holds iff origin z_(1) " and " z_(2) are collinear and z_(1),z_(2) lie on the same side of the origin . If abs(z-(1)/(z))=2 and sum of greatest and least values of abs(z) is lambda , then lambda^(2) , is

For any two complex numbers z_(1) "and" z_(2) , abs(z_(1)-z_(2)) ge {{:(abs(z_(1))-abs(z_(2))),(abs(z_(2))-abs(z_(1))):} and equality holds iff origin z_(1) " and " z_(2) are collinear and z_(1),z_(2) lie on the same side of the origin . If abs(z-(2)/(z))=4 and sum of greatest and least values of abs(z) is lambda , then lambda^(2) , is

For any two complex numbers z_(1) "and" z_(2) , abs(z_(1)-z_(2)) ge {{:(abs(z_(1))-abs(z_(2))),(abs(z_(2))-abs(z_(1))):} and equality holds iff origin z_(1) " and " z_(2) are collinear and z_(1),z_(2) lie on the same side of the origin . If abs(z-(3)/(z))=6 and sum of greatest and least values of abs(z) is 2lambda , then lambda^(2) , is

If |z|ge3, then determine the least value of |z+(1)/(z)| .

If |z-i|le5andz_(1)=5+3i("where",i=sqrt(-1), the greatest and least values of |iz+z_(1)| are

Find the gratest and the least values of |z_(1)+z_(2)|, if z_(1)=24+7iand |z_(2)|=6," where "i=sqrt(-1)

If |z+(4)/(z)|=2, find the maximum and minimum values of |z|.

If yz+zx+xy=12 , where x,y,z are positive values find the greatest value of xyz.