If `|z^2+1|=|z|`such that `arg z in [k pi, m pi]` where `k,m gt 0` then maximum value of `1/k+2/m` is

If |z^(2)+1|=|z| where arg(z)>0&arg z in[k pi,m pi], then (1)/(k)+(2)/(m) is equal to

If |z_1| = |z_2| and "arg" (z_1) + "arg" (z_2) = pi//2, , then

Let z_(1) and Z_(2) be two complex numbers such that |z_(1)|=1 and |z_(2)|=10. If theta=arg((z_(1)-z_(2))/(z_(2))) then maximum value of tan^(2)theta can be expressed as (m)/(n) (where m and n are coprime ) .Find the value of (100m-n)

If |z-2-i|=|z|sin((pi)/(4)-arg z)|, where i=sqrt(-1) ,then locus of z, is

If 2pi//3 and pi//6 are the arguments of barz_1 and z_2 then value of arg (z_1//z_2) is

If arg(z - 1) = pi/6 and arg(z + 1) = 2 pi/3 , then prove that |z| = 1 .

Let z_1, z_2,z_3 be complex numbers (not all real) such that |z_1|=|z_2|=|z_3|=1 and 2(z_1+z_2+z_3)-3z_1 z_2 z_3 is real. Then, Max (arg(z_1), arg(z_2), arg(z_3)) (Given that argument of z_1, z_2, z_3 is possitive ) has minimum value as (kpi)/6 where (k+2) is

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then find the of z_(1)z_(2).

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then find the of z_(1)z_(2).