Multiple Choice QuestionsIf z is a complex number of unit modulus and argument θ, then arg 
is equal to
-θ
π/2-θ
θ
θ
The equation esinx-e-sinx -4 = 0 has
infinite number of real roots
No real root
exactly one real root
exactly one real root
Let α, β be real and z be a complex number. If z2 + αz + β = 0 has two distinct roots on the line Re z = 1, then it is necessary that
β ∈(0, 1)
β ∈(-1, 0)
|β| = 1
|β| = 1
If ω(≠1) is a cube root of unity, and (1 + ω)7 = A + Bω.Then (A, B) equals
(0,1)
(1,1)
(1,0)
(1,0)
If α and β are the roots of the equation x2 – x +1 =0, then α2009 + β2009 =
-2
-1
1
1
C.
1
The quadratic equation ax2 + bx +c = 0 has roots α and β,
Then α + β = - b/a, α β = c/a
Also, if ax2+ bx +c = 0
Then, 
We know that 1,ω, ω2 are cube roots of unity.
1+ω + ω2 = 0 (ω2 = 1)
and 
Since α and β are roots of the equations
x2-x+1 = 0
⇒ α + β = 1 , α β =1
x = ω2, or -ω
α = -ω2, then β =-ω
or α = -ω, then β =-ω2, (where ω3 = 1)
Hence, α2009 + β2009 =(-ω)2009 + (-ω2)2009
= - [(ω3)669. ω2 + (ω3)1337.ω]
= - [ω2 + ω]
= -(-1) = 1
If, for a positive integer n, the quadratic equation,
x(x + 1) + (x + 1) (x + 2) + .....
+ (x + n -1 ) (x + n) = 10n
has two consecutive integral solutions, then n is equal to :
11
12
9
9
If the roots of the equation bx2+ cx + a = 0 be imaginary, then for all real values of x, the expression 3b2x2 + 6bcx + 2c2 is
greater than 4ab
less than 4ab
greater than -4ab
greater than -4ab
The quadratic equations x2 – 6x + a = 0 and x2 – cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is
1
4
3
3
Switch
. Then the complex number is
