Complex Number MSQ

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*Multiple options can be correct

Complex Number MSQ - Question 1

If n is the smallest positive integer for which where a > 0 and b > 0 then the numerical value of b/a is :

A.
B.
C.
3
D.
√3

Detailed Solution for Complex Number MSQ - Question 1

n = 1 ⇒ b = 0 not possible
n = 2 ⇒ a = 0 or b = 0 not possible
n = 3 ⇒ a³ - ib³ + 3a²bi - 3ab² = a³ + ib³ -3a²bi - 3ab²
The correct answers are:

*Multiple options can be correct

Complex Number MSQ - Question 2

If α,β be the roots o f the equation μ² - 2μ + 2 = 0 and if cot θ = x + 1, then is equal to :

Detailed Solution for Complex Number MSQ - Question 2

The correct answers are:

*Multiple options can be correct

Complex Number MSQ - Question 3

The complex numbers associated with the vertices A, B, C of Δ ABC are e^iθ, ω,ω²respectively, where ω is imaginary cube root of unity and cos θ > Re (ω), then the complex number representing the point where angle bisector of ∠ A meets the circumcircle of triangle, is :

A.
e^iθ
B.
ω + ω²
C.
e^-iθ
D.
-1

Detailed Solution for Complex Number MSQ - Question 3

⇒ A lies on major are BC

∴ angle subtended by are at O

The correct answers are: ω + ω²,-1

*Multiple options can be correct

Complex Number MSQ - Question 4

If ω is an imaginary cube root of unity such that and
then

A.
1
B.
3
C.
2
D.
4

Detailed Solution for Complex Number MSQ - Question 4

ω and ω² are roots of the equation

sum of roots = ω + ω^{2 +}α = 0
⇒ α = 1
⇒
The correct answers are: 2, 3, 4

*Multiple options can be correct

Complex Number MSQ - Question 5

Which of the following statement are true.

A.
are two pairs of non zero conjugate complex numbers then
B.
is an imaginary fifth root of unity, then 1
C.
are two of the 8th roots of unity, such that is least positive, then
D.
The product of all the fifth roots o f - 1 is equal to - 1

Detailed Solution for Complex Number MSQ - Question 5

S₃ : Since z₁ z₂ are 8th roots of unity

∴ product of all the roots = (-1)^5 . 1 = -1
The correct answers are: S₂ : If ω is an imaginary fifth root of unity, then If z₁ and z₂ are two of the 8th roots o f unity, such that is least positive, then S₄ : The product of all the fifth roots of-1 is equal to-1

*Multiple options can be correct

Complex Number MSQ - Question 6

If z₁ lies on |z| = 1 and z₂ lies on |z| = 2, then :

Detailed Solution for Complex Number MSQ - Question 6

The correct answers are: , ,,

*Multiple options can be correct

Complex Number MSQ - Question 7

lf then roots of the equation are:

A.
z₀
B.
2
C.
2,
D.

Detailed Solution for Complex Number MSQ - Question 7

The correct answers are: z₀,2,

*Multiple options can be correct

Complex Number MSQ - Question 8

Let z₁,and z₂ be non-zero complex numbers satisfying Then the triangle made by points with vertices at origin, z₁ and z₂ is :

A.
an equilateral triangle
B.
an isosceles triangle
C.
a right angled isosceles triangle
D.
triangle is neither isosceles nor right angle

Detailed Solution for Complex Number MSQ - Question 8

The correct answers are: an isosceles triangle, a right angled isosceles triangle

*Multiple options can be correct

Complex Number MSQ - Question 9

If z is a complex number satisfying then z lies on :

A.
y = x
B.
y = - x + 1
C.
y = x + 1
D.
y = - x

Detailed Solution for Complex Number MSQ - Question 9

The correct answers are: y = x, y = - x

*Multiple options can be correct

Complex Number MSQ - Question 10

If z₁ = 5 + 12i and |z₂| = 4 then :

A.
minimum
B.
minimum
C.
maximum
D.
maximum

Detailed Solution for Complex Number MSQ - Question 10

z₁ 5 + 12i,|z₂| = 4

The correct answers are: maximum maximum

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10 Questions MCQ Test Topic wise Tests for IIT JAM Physics | Complex Number MSQ

If n is the smallest positive integer for which where a > 0 and b > 0 then the numerical value of b/a is :

If α,β be the roots o f the equation μ² - 2μ + 2 = 0 and if cot θ = x + 1, then is equal to :

The complex numbers associated with the vertices A, B, C of Δ ABC are e^iθ, ω,ω²respectively, where ω is imaginary cube root of unity and cos θ > Re (ω), then the complex number representing the point where angle bisector of ∠ A meets the circumcircle of triangle, is :

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Complex Number MSQ

10 Questions MCQ Test Topic wise Tests for IIT JAM Physics | Complex Number MSQ

If n is the smallest positive integer for which where a > 0 and b > 0 then the numerical value of b/a is :

If α,β be the roots o f the equation μ2 - 2μ + 2 = 0 and if cot θ = x + 1, then is equal to :

The complex numbers associated with the vertices A, B, C of Δ ABC are eiθ, ω,ω2 respectively, where ω is imaginary cube root of unity and cos θ > Re (ω), then the complex number representing the point where angle bisector of ∠ A meets the circumcircle of triangle, is :

Topic wise Tests for IIT JAM Physics

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Topic wise Tests for IIT JAM Physics

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If α,β be the roots o f the equation μ² - 2μ + 2 = 0 and if cot θ = x + 1, then is equal to :

The complex numbers associated with the vertices A, B, C of Δ ABC are e^iθ, ω,ω²respectively, where ω is imaginary cube root of unity and cos θ > Re (ω), then the complex number representing the point where angle bisector of ∠ A meets the circumcircle of triangle, is :