हिंदी

Find the value of ω18 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find the value of ω18

योग

उत्तर

ω3 = 1

ω18 = (ω3)6

= (1)6

= 1

shaalaa.com
Cube Root of Unity
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Complex Numbers - Exercise 1.4 [पृष्ठ २०]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 1 Complex Numbers
Exercise 1.4 | Q 1. (i) | पृष्ठ २०

संबंधित प्रश्न

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`.


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, show that (2 − ω)(2 − ω2) = 7


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


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 α4 + β4 + α−1β−1 = 0


Find the equation in cartesian coordinates of the locus of z if |z| = 10


Find the equation in cartesian coordinates of the locus of z if |z − 5 + 6i| = 5


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" + 3"i")/("z" - 6"i")|` = 1


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 :


Answer the following:

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


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)` = ______.


Simplify the following and express in the form a + ib.

`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`


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 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:

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


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×
Our website is made possible by ad-free subscriptions or displaying online advertisements to our visitors.
If you don't like ads you can support us by buying an ad-free subscription or please consider supporting us by disabling your ad blocker. Thank you.