Solution:
SOLUTION
pth root of unity lies at an angle difference of 2π/ p on a unit circle in argand plane.
Similarly qth root of unity lies on a difference of 2π /q angle on unit circle.
Since P and q are prime therefore 2πk/p and 2πm / q are not same for any +ve integer k and m.
Thus only common pth and qth root is 1 which is not imaginary.Thus no common imaginary root is possible.
