State true or false for the following.
If z is a complex number such that ` z ne 0 " and Re " (z)= 0 " then Im" (z^(2)) = 0` .

If z is a complex numbers such that z ne 0 and "Re"(z)=0 , then

If z is a complex number such that Re(z)=Im(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.

State true or false for the following. For any complex number z, the minimum value of |z| + |z-1| is 1 .

Find the complex number z such that z^2+|z|=0

z is a complex number such that |Re(z)| + |Im (z)| = 4 then |z| can't be

for a complex number z, Show that |z|=0 z=0

State true or false for the following. Let z_(1) " and " z_(2) be two complex numbers such that |z_(2) + z_(2)| = |z_(1) | + |z_(2)| , then arg (z_(1) - z_(2)) = 0