Let `Z` be a complex number such that `|2Z+(1)/(Z)|=1` and `arg Z=theta` then minimum value of `8sin^(2)theta` is

Let z be a complex number such that |5z+(1)/(z)|=3 and arg(z)=theta ,then maximum value of cos(2 theta) is -

Let Z and w be two complex number such that |zw|=1 and arg(z)-arg(w)=pi/2 then

If z be the complex number such that |z+(1)/(z)|=2 then minimum value of (|z|)/(tan((pi)/(8))) is

If z is a complex number such that |z|>=2 then the minimum value of |z+(1)/(2)| is

Let Z_(1) and Z_(2) be two complex numbers satisfying |Z_(1)|=9 and |Z_(2)-3-4i|=4 . Then the minimum value of |Z_(1)-Z_(2)| is

For a complex number Z,|Z|=1 and "arg "(Z)=theta . If (Z)(Z^(2))(Z^(3))…(Z^(n))=1 , then the value of theta is

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_(1) and z_(2) are two non-zero complex number such that |z_(1)z_(2)|=2 and arg(z_(1))-arg(z_(2))=(pi)/(2) ,then the value of 3iz_(1)z_(2)

Let z_1 and z_2 be two complex numbers satisfying |z_1|=9 and |z_2-3-4i|=4 Then the minimum value of |z_1-Z_2| is