If `omega ` is the imaginary cube roots of unity, then the number of pair of integers (a,b) such that `|aomega + b| = 1` is ______.

Answer

6

Explanation

We have `|aomega + b| = 1`
`rArr |aomega + b|^(2) =1`
`rArr (aomega + b)(abaromega +b) = 1`
`rArr a^(2) + ab (omega + baromega) +b^(2) =1`
`rArr a^(2) -ab + b^(2)=1`
`rArr (a-b)^(2)+ab = 1" "(1)`
When `(a-b)^(2) = 0` and ab = 1, `then (1,1),(-1,-1)`
when `(a-b)^(2) = 1 and ab = 0`, then `(0,1),(1,0),(0,-1),(-1,0)`
Hence, there are 6 ordered pairs.