If a and b are real numbers such that `(2+alpha)^(4)=a+balpha`, where `alpha=(-1+isqrt3)/(2)`, then `a+b` is equal to:

if (1+tan alpha)(1+tan4 alpha)=2 where alpha in(0,(pi)/(16)) then alpha equal to

If (1+isqrt3)^9 = a+ib , then value of b is equal to

if (1+tan alpha )(1+tan4 alpha ) =2 where alpha in (0 , pi/16 ) then alpha equal to

Let f (x) = log _e (sinx ), ( 0 lt x lt pi ) and g(x) = sin ^(-1) (e ^(-x)), (x ge 0) . If alpha is a positive real number such that a = ( fog)' ( alpha ) and b = (fog ) ( alpha ) , then (A) aalpha ^(2) - b alpha - a = 0 (B) a alpha ^(2) - b alpha - a = 1 (C) a alpha ^(2) + b alpha - a = - 2 alpha ^(2) (D) a alpha ^(2) + b alpha + a = 0

Let a and b are non-zero real numbers and alpha^(3)+beta^(3)=-a,alpha beta=b then the quadratic equation whose roots are (alpha^(2))/(beta),(beta^(2))/(alpha) is

I: If a and b are positive real numbers then sqrt(-a) xx sqrt(-b) = -sqrt(ab) II : The Arg [(1 + isqrt3)/(1 - isqrt3)] is 240^(@) Which of the statements are true

If alpha_(1),alpha_(2),alpha_(3), alpha_(4) are the roos of x^(4)+2x^(3)+bx^(2)+cx+d=0 such that alpha_(1)-alpha_(3)=alpha_(4)-alpha_(2) , then b-c is equal to__________

If alpha_(1),alpha_(2),alpha_(3), alpha_(4) are the roos of x^(4)+2x^(3)+bx^(2)+cx+d=0 such that alpha_(1)-alpha_(3)=alpha_(4)-alpha_(2) , then b-c is equal to__________

The number of pairs (a, b) of real numbers, such that whenever alpha is a root of the equation x^2 +ax + b = 0, alpha^2 - 2 is also a root of this equation, is :