Advertisements
Advertisements
प्रश्न
If ω is a complex cube root of unity, find the value of ω2 + ω3 + ω4.
Advertisements
उत्तर
ω is a complex cube root of unity
∴ ω3 = 1 and 1 + ω + ω2 = 0
Also, 1 + ω2 = - ω, 1 + ω = - ω2 and ω + ω2 = – 1
ω2 + ω3 + ω4
= ω2 (1 + ω + ω2) = ω2(0) = 0
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, 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 ω–30
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 `ω + 1/ω`
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 + 8| = |z – 4|
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`
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 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, 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, then prove the following.
(w2 + w - 1)3 = - 8
