If least positive argument of `z` satisfying `z^(12)+9z^(6)-400=0` is `theta`, then value of `4cos^(2)theta` is

If theta be a positive acute angle satisfying cos^(2)theta+cos^(4)theta=1 , then the value of tan^(2)theta+tan^(4)theta is

If z is a complex number satisfying |z|^(2)-|z|-2 lt 0 , then the value of |z^(2)+zsintheta| , for all values of theta , is

If z is a complex number satisfying the equaiton z^(6) - 6z^(3) + 25 = 0 , then the value of |z| is

Smallest positive value of theta satisfying 8sin theta cos2 theta sin3 theta cos4 theta=cos6 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 be a complex number such that |2Z+(1)/(Z)|=1 and arg Z=theta then minimum value of 8sin^(2)theta is

If z is a complex number satisfying z^(4)+z^(3)+2z^(2)+z+1=0 then the set of possible values of z is

Let z be a complex number having the argument theta,0

If z is a complex number satisfying the equation z^(6)+z^(3)+1=0. If this equation has a root re^(i theta) with 90^(@)<0<180^(@) then the value of theta is

theta in [0,2pi] and z_(1) , z_(2) , z_(3) are three complex numbers such that they are collinear and (1+|sin theta|)z_(1)+(|cos theta|-1)z_(2)-sqrt(2)z_(3)=0 . If at least one of the complex numbers z_(1) , z_(2) , z_(3) is nonzero, then number of possible values of theta is