If `alpha` is a complex constant such that `alpha z^2+z+ baralpha=0` has a real root, then (a) `alpha+ bar alpha=1` (b) `alpha+ bar alpha=0` (c)`alpha+ bar alpha=-1` (d)the absolute value of the real root is 1

If alpha is a complex constant such that alpha^(2)+z+bar(alpha)=0 has a real root then

If alpha is a complex number and x^(2)+alpha x+bar(alpha)=0 has a real root lambda then lambda=

If alpha=(z)/(bar(z)), then | alpha|

If alpha is a non-real root of x^(6)=1 then (alpha^(5)+alpha^(3)+alpha+1)/(alpha^(2)+1)=

If alpha is a non real root of x^(6)=1 then alpha^(5)+alpha^(3)+alpha+1hline alpha^(2)+1

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

If a cos alpha+i sin alpha and the equation az^(2)+z+1=0 has a pure imaginary root, then tan alpha=

If alpha is non real fifth root of unity then alpha^(101)+alpha^(102)+alpha^(103)+alpha^(104)+alpha^(105) is

If alpha is a non-real fifth root of unity, then the value of 3^(|1+alpha+alpha^(2),alpha^(-2)-alpha^(-1)| , is