English

Find the value of ω18 - Mathematics and Statistics

Advertisements
Advertisements

Question

Find the value of ω18

Sum

Solution

ω3 = 1

ω18 = (ω3)6

= (1)6

= 1

shaalaa.com
Cube Root of Unity
  Is there an error in this question or solution?
Chapter 1: Complex Numbers - Exercise 1.4 [Page 20]

RELATED QUESTIONS

If `omega` is a complex cube root of unity, show that `(2 - omega)(2 - omega^2)` = 7


If ω is a complex cube root of unity, find the value of `omega + 1/omega`


If ω is a complex cube root of unity, find the value of (1 + ω2)3


If `omega` is a complex cube root of unity, find the value of `(1 + omega)(1 + omega^2)(1 + omega^4)(1 + omega^8)`


If α and β are the complex cube roots of unity, show that α2 + β2 + αβ = 0.


If x = a + b, y = αa + βb and z = aβ + bα, where α and β are the complex cube roots of unity, show that xyz = a3 + b3.


If ω is a complex cube root of unity, then prove the following: (ω2 + ω - 1)3 = – 8


If ω is a complex cube root of unity, then prove the following:  (a + b) + (aω + bω2) + (aω2 + bω) = 0.


Find the value of ω21


Find the value of ω–105


If ω is a complex cube root of unity, show that (1 + ω − ω2)6 = 64


If ω is a complex cube root of unity, show that (1 + ω)3 − (1 + ω2)3 = 0


If ω is a complex cube root of unity, show that (a − b) (a − bω) (a − bω2) = a3 − b3


If ω is a complex cube root of unity, find the value of ω2 + ω3 + ω4


If ω is a complex cube root of unity, find the value of (1 − ω − ω2)3 + (1 − ω + ω2)3


If α and β are the complex cube root of unity, show that α2 + β2 + αβ = 0


If , where α and β are the complex cube-roots of unity, show that xyz = a3 + b3.


Find the equation in cartesian coordinates of the locus of z if |z – 3| = 2


Find the equation in cartesian coordinates of the locus of z if |z + 8| = |z – 4|


Select the correct answer from the given alternatives:

If ω is a complex cube root of unity, then the value of ω99+ ω100 + ω101 is :


If ω is the cube root of unity then find the value of `((-1 + "i"sqrt(3))/2)^18 + ((-1 - "i"sqrt(3))/2)^18`


Which of the following is the third root of `(1 + i)/sqrt2`? 


If α, β, γ are the cube roots of p (p < 0), then for any x, y and z, `(xalpha + "y"beta + "z"gamma)/(xbeta + "y"gamma + "z"alpha)` = ______.


If w is a complex cube root of unity, show that

`((a + bw + cw^2)) /( c + aw + bw^2 )= w^2`


If ω is a complex cube-root of unity, then prove the following:

(a + b) + (aω + bω2) + (aω2 + bω) = 0


If w is a complex cube root of unity, show that `((a + bω + cω^2))/(c + aω + bω^2) = ω^2`


Find the value of `sqrt(-3) xx sqrt(-6)`.


If w is a complex cube-root of unity, then prove the following

(w2 + w - 1)3 = - 8


If ω is a complex cube-root of unity, then prove the following:

2 + ω − 1)3 = −8


 Find the value of `sqrt(-3)xx sqrt (-6)`


If w is a complex cube root of unity, show that `((a+bw+cw^2))/(c+aw+bw^2) = w^2`


If w is a complex cube-root of unity, then prove the following. 

(w+ w - 1)= - 8


If ω is a complex cube root of unity, show that `((a + bomega + comega^2))/(c + aomega + bomega^2)=omega^2`


If ω is a complex cube-root of unity, then prove the following.

2 + ω − 1)3 = −8


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×