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

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 :

Advertisements
Advertisements

प्रश्न

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 :

पर्याय

  • −1

  • 1

  • 0

  • 3

MCQ
Advertisements

उत्तर

0

Explanation:

ω99+ ω100 + ω101

= ω99 (1 + ω + ω2)

= ω99 (0)

= 0

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Complex Numbers - Miscellaneous Exercise 1.1 [पृष्ठ २१]

APPEARS IN

बालभारती Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
पाठ 1 Complex Numbers
Miscellaneous Exercise 1.1 | Q I. (4) | पृष्ठ २१

संबंधित प्रश्‍न

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 ω2 + ω3 + ω4.


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 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.


Find the value of ω21


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, show that (a − b) (a − bω) (a − bω2) = a3 − b3


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


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


If ω(≠1) is a cube root of unity and (1 + ω)7 = A + Bω, then A and B are respectively the numbers ______.


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`


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 ______.


The value of the expression 1.(2 – ω) + (2 – ω2) + 2.(3 – ω)(3 – ω2) + ....... + (n – 1)(n – ω)(n – ω2), where ω is an imaginary cube root of unity is ______.


If the cube roots of the unity are 1, ω and ω2, then the roots of the equation (x – 1)3 + 8 = 0, are ______.


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:

(a + b) + (aω + bω2) + (aω2 + bω) = 0


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:

(ω2 + 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 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. 

(w2 + w - 1)3 = - 8


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×