The number of common roots of the 15th and  of 25th roots of unity are
  • A
    1
  • A
    1
  • B
    5
  • B
    5
  • C
    6
  • C
    6
  • D
    10
  • D
    10

Solution

$$15th$$ roots of unity are $$e^{\dfrac{{i}2{k}\pi}{15}}$$ where $$k=1,2,\cdots,15$$
$$25th$$ roots of unity are $$e^{\dfrac{{i}2{m}\pi}{25}}$$ where $$m=1,2,3,\cdots,25$$
The common roots are $$e^{i\dfrac{2{n}}{5}}$$ where $$n=1,2,3,4,5$$
Number of common roots will be $$5$$