Advertisements
Advertisements
प्रश्न
If `omega` is a complex cube root of unity, show that `(2 - omega)(2 - omega^2)` = 7
Advertisements
उत्तर
`omega` is a complex cube root of unity.
∴ `omega^3 = 1 and 1 + omega + omega^2` = 0
Also, `1 + omega^2 = -omega, 1 + omega = - omega^2 and omega + omega^2` = – 1
L.H.S. = `(2 - omega)(2 - omega^2)`
= `4 - 2omega^2 - 2omega + omega^3`
= `4 - 2(omega^2 + omega) + 1`
= 4 – 2(– 1) + 1
= 4 + 2 + 1
= 7
= R.H.S.
APPEARS IN
संबंधित प्रश्न
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
Find the value of ω–105
If ω is a complex cube root of unity, show that `("a" + "b"ω + "c"ω^2)/("c" + "a"ω + "b"ω^2)` = ω2
If ω is a complex cube root of unity, find the value of (1 − ω − ω2)3 + (1 − ω + ω2)3
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 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:
(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 ω 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 + bω + cω^2))/(c + aω + bω^2) = ω^2`
If ω 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 + bomega + comega^2))/(c + aomega + bomega^2) = w^2`
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`
