For any two complex numbers, `z_(1),z_(2)`
`|1/2(z_(1)+z_(2))+sqrt(z_(1)z_(2))|+|1/2(z_(1)+z_(2))-sqrt(z_(1)z_(2))|` is equal to

For any two complex numbers z_(1) and z_(2) , prove that Re ( z_(1)z_(2)) = Re z_(1) Re z_(2)- 1mz_(1) Imz_(2)

If z_(1),z_(2),z_(3) are complex numbers such that : |z_(1)|=|z_(2)|=|z_(3)|=|(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))|=1 , then |z_(1)+z_(2)+z_(3)| is equal to

|z_(1)+z_(2)|=|z_(1)|+|z_(2)| is possible if

The complex numbers z_(1), z_(2), z_(3) satisfying (z_(1)-z_(3))/(z_(2)-z_(3))=(1-i sqrt(3))/(2) are the vertices of a triangle which is

If z^(1) =2 -I, z_(2)=1+i , find |(z_(1) + z_(2) + 1)/(z_(1)-z_(2) + 1)|

If z_(1),z_(2) are two complex numbers satisfying the equation : |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then (z_(1))/(z_(2)) is a number which is

If z_(1) and z_(2) are two non-zero complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| , then arg. z_(1)- arg. z_(2) equals :

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then find z_(1)+z_(2) .

For all complex numbers z_(1), z_(2) satisfying |z_(1)|=12 and |z_(2)-3-4 i|=5 , the minimum value of |z_(1)-z_(2)| is

Let z_(1) =2-I, z_(2) =-2 + i , Find (i) (Re(z_(1)z_(2))/barz_(1)) , (ii) Im(1/(z_(1)barz_(1)))