Let `z_(1),z_(2)` be two complex numbers such that `|z_(1)+z_(2)|=|z_(1)|+|z_(2)|`. Then,

State true of false for the following: Let z_(1) and z_(2) be two complex number's such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| then arg (z_(1)-z_(2))=0

Let z_(1) and z_(2) be two complex numbers such that |z_(1)+z_(2)|^(2)=|z_(1)|^(2)+|z_(2)|^(2) . Then,

State ture or false for the following. (i) The order relation is defined on the set of complex numbers. (ii) Multiplication of a non-zero complex number by -i rotates the point about origin through a right angle in the anti-clockwise direction.(iiI) For any complex number z, the minimum value of |z|+|z-1| is 1. (iv) The locus represent by |z-1|= |z-i| is a line perpendicular to the join of the points (1,0) and (0,1) . (v) If z is a complex number such that zne 0" and" Re (z) = 0, then Im (z^(2)) = 0 . (vi) The inequality |z-4|lt |z-2| represents the region given by xgt3. (vii) Let z_(1) "and" z_(2) be two complex numbers such that |z_(1)+z_(2)|= |z_(1)+z_(2)| ,then arg (z_(1)-z_(2))=0 . 2 is not a complex number.

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

Consider z_(1)andz_(2) are two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| Statement -1 amp (z_(1))-amp(z_(2))=0 Statement -2 The complex numbers z_(1) and z_(2) are collinear.

Consider z_(1)andz_(2) are two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| Statement -1 amp (z_(1))-amp(z_(2))=0 Statement -2 The complex numbers z_(1) and z_(2) are collinear. Check for the above statements.

Consider z_(1)andz_(2) are two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| Statement -1 arg (z_(1))-arg(z_(2))=0 Statement -2 The complex numbers z_(1) and z_(2) are collinear.

Consider z_(1)andz_(2) are two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| Statement -1 amp (z_(1))-amp(z_(2))=0 Statement -2 The complex numbers z_(1) and z_(2) are collinear. Check for the above statements.