If `z!=0` is a complex njmber, then prove that `R e(z)=0 rArr Im(z^2)=0.`

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

For any complex number z prove that |Re(z)|+|Im(z)|<=sqrt(2)|z|

If z is a complex number such that Re(z)=Im(2), then

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

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

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 .

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