If ` |z +1| = z + 2(1 - i) ` , then the value of z

If |z - 1| = |z + 1| = |z - 2i|, then value of |z| is

If z_1 = 3i and z_2 = -1 -i , find the value of arg z_1/z_2 .

If | (z - i)/(z + 2i)| = 1, |z| = 5/2 then the value of |z + 3i|

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 z_(1) + z_(2) + z_(3) = 0 and |z_(1)| = |z_(2)| = |z_(3)| = 1 , then value of z_(1)^(2) + z_(2)^(2) + z_(3)^(2) equals

If z=(1)/(2)(i sqrt(3)-1), then find the value of (z-z^(2)+2z^(3))(2-z+z^(2))

Let z_(1), z_(2) are complex numbers and |z_(1)|=2 and (1-i)z_(2)+(1+i) z_(2)= K sqrt(2),K>0 such that the minimum value of |z_(1)-z_(2)| equals 2 then the value of |K| equals