Advertisements
Advertisements
प्रश्न
If ω is a complex cube root of unity, show that `((a + bomega + comega^2))/("c" + aomega + bomega^2) = omega^2`.
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
L.H.S. = `(a + bomega + comega^2)/(c + aomega + bomega^2)`
= `(aomega^3 + bomega^4 + comega^2)/(c + aomega + bomega^2) ...[∵ omega^3 = 1, omega^4 = omega]`
= `(omega^2(c + aomega + bomega^2))/(c + aomega + bomega^2)`
= ω2
= R.H.S.
APPEARS IN
संबंधित प्रश्न
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
Find the value of ω21
Find the value of ω–30
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, show that (a + b)2 + (aω + bω2)2 + (aω2 + bω)2 = 6ab
If ω is a complex cube root of unity, find the value of (1 + ω2)3
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 – 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 α and β are complex cube roots of unity, prove that (1 − α)(1 − β) (1 − α2)(1 − β2) = 9.
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 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 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, then prove the following.
(w2 + w - 1)3 = - 8
