The complex numbers sinxicos2x and cosxisin2x are conjugate to each other when

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VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 2>Q 8

A regular hexagon is drawn with two of its vertices forming a shorter diagonal at

z = - 2

and

z = 1 - i \sqrt{3} .

The other four vertices are

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IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 2>Q 9

If

x = \cos α + i \sin α, y = \cos β + i \sin β, z = \cos γ + i \sin γ

and

x + y + z = x y z,

then

Σ \cos (β - γ)

equals

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IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 2>Q 10

If

α, β

are the roots of the equation

a x^{2} + b x + c = 0

and

S_{n} = α^{n} + β^{n},

then

a S_{n + 1} + c S_{n - 1} =

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VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 2>Q 11

If

x = a + b, y = a ω + b ω^{2}

and

z = a ω^{2} + b ω,

then

x^{3} + y^{3} + z^{3}

is equal to

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VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 2>Q 12

Square root of

- 8 - 6 i

is

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VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 2>Q 13

If the complex numbers $z_{1}, z_{2}$ and $z_{3}$ are in $A . P .,$ then they lie on a

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VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 2>Q 14

If

{(1 + x + x^{2})}^{n} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{2 n} x^{2 n},

then the value of

a_{0} + a_{3} + a_{6} + \dots

is

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VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 2 - Complex Numbers>Exercise 2>Q 15

If

α, β

are the roots of

x^{2} + p x + q = 0,

and

w

is an imaginary cube root of unity, then value of

(w α + w^{2} β) (w^{2} α + w β)

is

The complex numbers $\sin x + i \cos 2 x$ and $\cos x - i \sin 2 x$ are conjugate to each other when

Important Questions on Complex Numbers

Learn and Prepare for any exam you want !

The complex numbers sinx+icos2x and cosx-isin2x are conjugate to each other when

Important Questions on Complex Numbers

Learn and Prepare for any exam you want !

The complex numbers $\sin x + i \cos 2 x$ and $\cos x - i \sin 2 x$ are conjugate to each other when