Advertisements
Advertisements
प्रश्न
If ω is a complex cube root of unity, find the value of `omega + 1/omega`
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
`omega + 1/omega = (omega^2 + 1)/omega = (-omega)/omega` = – 1.
APPEARS IN
संबंधित प्रश्न
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"omega + "c"omega^2))/("c" + "a"omega + "b"omega^2) = omega^2`.
If α and β are the complex cube roots of unity, show that α2 + β2 + αβ = 0.
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–30
Find the value of ω–105
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
Find the equation in cartesian coordinates of the locus of z if |z + 8| = |z – 4|
Which of the following is the third root of `(1 + i)/sqrt2`?
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
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 + bω + cω^2))/(c + aω + bω^2) = ω^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, then prove the following:
(ω2 + ω − 1)3 = −8
Find the value of `sqrt(-3)xx sqrt (-6)`
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`
