If `pa n dq` are distinct prime numbers, then the number of distinct imaginary numbers which are pth as well as qth roots of unity are. `min(p ,q)` b. `min(p ,q)` c. `1""` d. `z e ro`

Options

A. min(p,q)
B. max(p,q)
C. 1
D. zero

Answer

D

Explanation

We have,
`e^((2piri)/(rho)) = e^((2pimi)/(q))`
`r = 0,1,.....,q-1`
`m = 0,1,......,q-1`
This in possible iff r=m = 0 but for r=m=0 we get 1 which is not an imaginary number.