Advertisements
Advertisements
Question
Find the value of ω–30
Solution
ω3 = 1
ω–30
= (ω3)–10
= (1)–10
= `1/(1)^10`
= 1
APPEARS IN
RELATED QUESTIONS
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 ω is a complex cube root of unity, find the value of (1 - ω - ω2)3 + (1 - ω + 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)(2 − ω2) = 7
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 (1 − ω − ω2)3 + (1 − ω + ω2)3
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 – 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(≠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 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`?
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 1, α1, α2, ...... αn–1 are the roots of unity, then (1 + α1)(1 + α2) ...... (1 + αn–1) is equal to (when n is even) ______.
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.
(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
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
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, then prove the following.
(w2 + w - 1)3 = - 8
If ω is a complex cube root of unity, show that `((a + bomega + comega^2))/(c + aomega + bomega^2)=omega^2`
