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

Let the cube root of 1 be ω i.e., 3√1 = ω.

⇒ ω3 = 1

⇒ ω3 – 1 = 0 or (ω – 1) (ω2 + ω + 1) = 0

So, either  ω – 1 = 0 or (ω2 + ω + 1) = 0

⇒ ω = 1 and (ω2 + ω + 1) = 0

Now, the roots of (ω2 + 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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