If A and B represent the complex numbers `z_1 and z_2` such that `|z_1-z_2|=|z_1+z_2|`, then circumcentre of `/_\AOB, O` being the origin is (A) `(z_1+2z_2)/3` (B) `(z_1+z_2)/3` (C) `(z_1+z_2)/2` (D) `(z_1-z_2)/3`

For any two complex number z_1a n d\ z_2 prove that: |z_1-z_2|lt=|z_1|+|z_2|

For any two complex number z_1a n d\ z_2 prove that: |z_1-z_2|geq|z_1|-|z_2|

For any two complex number z_1a n d\ z_2 prove that: |z_1+z_2|geq|z_1|-|z_2|

If for the complex numbers z_1 and z_2 , |z_1+z_2|=|z_1-z_2| , then Arg(z_1)-Arg(z_2) is equal to

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then

If z_1ne-z_2 and |z_1+z_2|=|1/z_1 + 1/z_2| then :

If z_1 and z_2 are complex numbers such that |z_1-z_2|=|z_1+z_2| and A and B re the points representing z_1 and z_2 then the orthocentre of /_\OAB, where O is the origin is (A) (z_1+z_2)/2 (B) 0 (C) (z_1-z_2)/2 (D) none of these

For any two complex numbers z_1 and z_2 prove that: |\z_1+z_2|^2=|\z_1|^2+|\z_2|^2+2Re bar z_1 z_2

If z_1 and z_2 are two complex numbers such that |\z_1|=|\z_2|+|z_1-z_2| show that Im (z_1/z_2)=0

Let z_1,z_2,z_3 be three distinct non zero complex numbers which form an equilateral triangle in the Argand pland. Then the complex number associated with the circumcentre of the tirangle is (A) (z_1 z_2)/z_3 (B) (z_1z_3)/z_2 (C) (z_1+z_2)/z_3 (D) (z_1+z_2+z_3)/3