The points represented by the complex numbers 1 + i , - 2 + 3 i , 5 3 i on the Argand diagram are

vertices of an equilateral triangle.

vertices of an isosceles triangle.

If is a cube root of unity thensin35252cos10234is

MEDIUM

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 4

If

x = ω - ω^{2} - 2,

where

ω & ω^{2}

are cube roots of unity, then the value of

x^{4} + 3 x^{3} + 2 x^{2} - 11 x - 6

is

MEDIUM

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 5

If

x + i y = {(1 - i \sqrt{3})}^{100},

then find

(x, y)

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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 6

The points represented by the complex numbers $1 + i, - 2 + 3 i, \frac{5}{3} i$ on the Argand diagram are

MEDIUM

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 7

The complex numbers

\sin x + i \cos 2 x

and

\cos x - i \sin 2 x

are conjugate to each other when

MEDIUM

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

MEDIUM

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 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

MEDIUM

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 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} =

MEDIUM

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

If $ω$ is a cube root of unity, then $\sin \{(ω^{35} + ω^{25}) π + \frac{π}{2}\} + \cos \{(ω^{10} + ω^{23}) π - \frac{π}{4}\}$ is

Important Questions on Complex Numbers

Learn and Prepare for any exam you want !

If ω is a cube root of unity, then sinω35+ω25π+π2+cosω10+ω23π-π4 is

Important Questions on Complex Numbers

Learn and Prepare for any exam you want !

If $ω$ is a cube root of unity, then $\sin \{(ω^{35} + ω^{25}) π + \frac{π}{2}\} + \cos \{(ω^{10} + ω^{23}) π - \frac{π}{4}\}$ is