Complex Number- 4 - Free MCQ Practice Test with solutions, JEE Chapter

Let  z(α,β) = cosα + e^iβ sinα (α, β ∈ R, i = √-1) then the exhaustive set of values of modulus of z(θ, 2θ), as θ varies, is 

If Z₁ ≠ - Z₂ and  then (Z₁, Z₂ ∈C)

If z = x + iy be a non real complex number and a₁ , a₂ , a₃ , b₁ , b₂ , b₃ are all real,then 

If  then the maximum value of |Z| is equal to

Let Z₁ = 10+ 6i and Z₂ = 4+6i . If Z be a complex number such that    Then |Z - 7 -9i| =

If a complex number Z satisfy, |2Z + 10 + 10i | < 5√3 - 5  then the least principal argument of Z is

If a,b,c are integers not all equal andw is a cube root of unity (ω ≠ 1) then the minimum value of |a + bω+ cω²| is

If 1, w, w² .....w^n-1 are n^th roots of 1 then value of   equals to

If 1, α₁, α₂ ,.......α₉₉ are roots of Z¹⁰⁰ = 1 then equal to

If cosx + 2cosy + 3cosz = sin x + 2siny + 3sinz = 0 then the value of sin 3x + 8sin 3y+ 27 sin 3z is 

Let a complex number z, with minimum argument is lying on the cure |z + 4i| = 2 then

Number of ordered pairs (a,b) of real numbers such that (a + ib)²⁰¹² = a - ib holds good is

If | z - 3i| = 3, (where i = √-1) and arg z ∈ (0, π/2), then cot (arg (z))  is equal to 

If α₀, α₁, α₂, ...α_n-1 be the nth roots of unity, then value of  is equal to

Let   then value of the determinant 

The least value of P for which the two curves arg z = π/6 and |z - 2 √3i| = P have a solution is ..

If |z -i| ≤ 2 and z₀ = 5+3i , the maximum value of  |iz + z₀| is

For all complex numbers z₁ ,z₂ satisfying |z₁| = 12 and |z₂ - 3 - 4i| = 5 , the minimum value of  |z1 -z2| is 

If b ≠ 1 be any n^th root of unity then 1 + 3β + 5β² + ........n terms equals 

The value of 

The number of solutions of the equation is

If a₁, a₂,--------a_n  are real numbers and cos α + isin α is a root of zⁿ +a₁z^n-1 + a₂z^n-2 +-----+a_n-1z+a_n = 0, then the value of a₁ cos α + a₂ cos 2α + a₃ cos 3α + ------ +a_n cos na is

If |z – 1| + |z + 3| ≤ 8, then the range of values of |z – 4| is,  

If a, b, c, a₁ , b₁ , c₁  are non zero complex numbers satisfying   and  

Let z and w be complex numbers such that   and arg zω =π, then arg z = 

Let z = cosθ + isinθ. Then the value of  at θ = 2° is

let a be a complex number such that |a| = 1 If the equation az² + z + 1 =0 has a pure imaginary root, then tan (arg a) =

 is purely imaginary, then number of values of a in [0, 2π ] is---

If z₁z₂ ∈ C,  and  = 11 then the value of is