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

If z=((sqrt3)/(2)+(1)/(2)i)^5+((sqrt3)/(2)-(i)/(2))^5 , then (a) im(z)=0 (b) Re(z)gt0 , Im(z)gt0 (c) Re(z)gt0 , Im(z)lt0 (d) Re(z)=3

If B: {z: |z-3-4i|}=5 and C={z:Re[(3+4i)z]=0} then the number of elements in the set B intesection C is (A) 0 (B) 1 (C) 2 (D) none of these

If z = 3 -2i then the value s of (Rez) (Im z)^(2) is

If z_0,z_1 represent points P ,Q on the locus |z-1|=1 and the line segment P Q subtends an angle pi/2 at the point z=1 then z_1 is equal to (a) 1+i(z_0-1) (b) i/(z_0-1) (c) 1-i(z_0-1) (d) i(z_0-1)

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

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

If 2+z+z^4=0, where z is a complex number then (A) 1/2 lt|z|lt1 (B) 1/2lt|z|lt1/3 (C) |z|ge1 (D) none of these

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

If z_(1)=2-i, z_(2)=1+ 2i, then find the value of the following : (i) Re((z_(1)*z_(2))/(bar(z)_(2))) (ii) Im (z_(1)*bar(z)_(2))

If arg(z) lt 0, then find arg(-z) -arg(z) .