The number of common roots of the 15th and of 25th roots of unity are
#### Solution

$$15th$$ roots of unity are $$e^{\dfrac{{i}2{k}\pi}{15}}$$ where $$k=1,2,\cdots,15$$

- A1
- A1
- B5
- B5
- C6
- C6
- D10
- D10

$$25th$$ 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 $$5$$