`|z-i|lt|z+i|` represents the region (A) `Re(z)gt0` (B) `Re(z)lt0` (C) `Im(z)gt0` (D) `Im(z)lt0`

The inequality |z-i| lt |z + i| represents the region

abs(z - 4 ) lt abs (z - 2) represents the region given by :

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 |u|=|v|=1uv!=-1 and z=(u-v)/(1+uv) then (a) |z|=1( b) Re(z)=0 (c) Im(z)=0 (d) Re(z)=Im(z)

Prove that Re (z_ (1) z_ (2)) = Re z_ (1) Rez_ (2) -Im z_ (1) Im z_ (2)

|z-4| 0 (b) Re(z) 3(d) None of these

If z=((sqrt(3))/(2)+(1)/(2)i)^(5)+((sqrt(3))/(2)-(i)/(2))^(5), then (a) im(z)=0 (b) Re(z)>0,Im(z)>0(c)Re(z)>0,Im(z)<0 (d) Re(z)=3

Let P point denoting a complex number z on the complex plane. i.e. z=Re(z)+i Im(z)," where "i=sqrt(-1) if" "Re(z)=x and Im(z)=y,then z=x+iy .The area of the circle inscribed in the region denoted by |Re(z)|+|Im(z)|=10 equal to