If `z_1 and z_2` both satisfy the relation `z+overlinez=2|z-1| and arg(z_1-z_2)=pi/4,` then `Im(z_1+z_2)` equals

z_(1)=3+I and z_(2)=-2+6i then find z_(1)z_(2)

z_(1)=4+3i and z_(2)=-8+5i then find z_(1)+z_(2) .

If |z| = 2 and arg z = (pi)/4 then z = ........

If z is a complex number satisfying the relation ∣z+1∣=z+2(1+i) then z is

z_(1)=9+3i and z_(2)=-2-i then find z_(1)-z_(2)

If z_1 and z_2 , are two non-zero complex numbers such tha |z_1+z_2|=|z_1|+|z_2| then arg(z_1)-arg(z_2) is equal to

Find the value of z satisfying the euqation |z|-z=1+2i .

locus of the point z satisfying the equation |z-1|+|z-i|=2 is

Find the point of intersection of the curves arg(z-3i)=(3pi)/4 and arg(2z+1-2i)=pi/4.