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.
are conjugate complex numbers which are also known as imaginary cube roots of unity.