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, show that `((a + bomega + comega^2))/("c" + aomega + bomega^2) = omega^2`.


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


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 ω–105


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, find the value of ω2 + ω3 + ω4


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


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


If ω is a complex cube root of unity, find the value of (1 + ω)(1 + ω2)(1 + ω4)(1 + ω8)


If α and β are the complex cube root of unity, show that α4 + β4 + α−1β−1 = 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| = 10


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|


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


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 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 w 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


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 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`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×