मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Find the value of ω18

Advertisements
Advertisements

प्रश्न

Find the value of ω18

बेरीज
Advertisements

उत्तर

ω3 = 1

ω18 = (ω3)6

= (1)6

= 1

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Complex Numbers - Exercise 1.4 [पृष्ठ २०]

APPEARS IN

संबंधित प्रश्‍न

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, show that (2 + ω + ω2)3 - (1 - 3ω + ω2)3 = 65


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 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–30


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 (3 + 3ω + 5ω2)6 − (2 + 6ω + 2ω2)3 = 0


If ω is a complex cube root of unity, show that (a + b) + (aω + bω2) + (aω2 + bω) = 0


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


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


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


Answer the following:

If ω is a complex cube root of unity, prove that (1 − ω + ω2)6 +(1 + ω − ω2)6 = 128


If (1 + ω2)m = (1 + ω4)m and ω is an imaginary cube root of unity, then least positive integral value of m is ______.


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)` = ______.


Let α be a root of the equation 1 + x2 + x4 = 0. Then the value of α1011 + α2022 – α3033 is equal to ______.


Let z = `(1 - isqrt(3))/2`, i = `sqrt(-1)`. Then the value of `21 + (z + 1/z)^3 + (z^2 + 1/z^2) + (z^3 + 1/z^3)^3 + ...... + (z^21 + 1/z^21)^3` is ______.


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, show that

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


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.

2 + ω −1)3 = −8


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, 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, show that `((a + b\omega + c\omega^2))/(c + a\omega + b\omega^2) = \omega^2`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×