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

For a complex number Z, if arg Z=(pi)/(4) and |Z+(1)/(Z)|=4 , then the value of ||Z|-(1)/(|Z|)| is equal to

For a complex number Z, if arg Z=(pi)/(4) and |Z+(1)/(Z)|=4 , then the value of ||Z|-(1)/(|Z|)| is equal to

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

Suppose z is a complex number such that z ne -1, |z| = 1 and arg(z) = theta . Let w = (z(1-bar(z)))/(bar(z)(1+z)) , then Re(w) is equal to

Suppose z is a complex number such that z ne -1, |z| = 1, and arg(z) = theta . Let omega = (z(1-bar(z)))/(bar(z)(1+z)) , then Re (omega) is equal to

Find the complex number z if arg (z+1)=(pi)/(6) and arg(z-1)=(2 pi)/(3)