What is cube root of unity i.e. omega???

Let the cube root of 1 be ω i.e.,

^{3}√1 = ω. ⇒ ω^{3} = 1

⇒ ω^{3} – 1 = 0 or (ω – 1) (ω^{2} + ω + 1) = 0

So, either ω – 1 = 0 or (ω^{2} + ω + 1) = 0

⇒ ω = 1 and (ω^{2} + ω + 1) = 0

Now, the roots of (ω^{2} + ω + 1) = 0 can be find out as follows:

ω =

So, we have ω = 1 and .

Hence, out of three cube roots of unity 1 is real number whereas other roots i.e., are conjugate complex numbers which are also known as imaginary cube roots of unity.

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