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)`

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

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

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), z_(2) are two complex numbers such that Im(z_(1)+z_(2))=0 and Im(z_(1) z_(2))=0 , then

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

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

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)))

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 :

A complex number z is said to be unimodular if |z| =1 suppose z_(1) and z_(2) are complex numebers such that (z_(1)-2z_(2))/(2-z_(1)z_(2)) is unimodular and z_(2) is not unimodular then the point z_(1) lies on a

Which of the following is correct for any two complex numbers z_(1) and z_(2) ?