Advertisements
Advertisements
Question
If ω is a complex cube root of unity, find the value of `omega + 1/omega`
Advertisements
Solution
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
RELATED QUESTIONS
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, then prove the following: (ω2 + ω - 1)3 = – 8
If ω is a complex cube root of unity, show that (1 + ω − ω2)6 = 64
If ω is a complex cube root of unity, show that (a + b) + (aω + bω2) + (aω2 + bω) = 0
If ω is a complex cube root of unity, find the value of `ω + 1/ω`
If ω is a complex cube root of unity, find the value of (1 − ω − ω2)3 + (1 − ω + ω2)3
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|
Find the equation in cartesian coordinates of the locus of z if `|("z" + 3"i")/("z" - 6"i")|` = 1
If α and β are complex cube roots of unity, prove that (1 − α)(1 − β) (1 − α2)(1 − β2) = 9.
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 ______.
Simplify the following and express in the form a + ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
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 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`
