Question

The equation zⁿ – 1 = 0 and z^m – 1 = 0 have only one common roots where m, n Ī N then –

• A. N and m are primes
• B. At least one of m and n is prime
• C. M and n are co-primes
• D. One out of m and n is even and other is odd

Answer 1

Answer: (C)

M and n are co-primes

Answer 2

Sol. zⁿ – 1 = 0, z^m – 1 = 0

z = cos $\frac{2p\pi}{n}$ + i sin $\frac{2p\pi}{n}$

& z = cos $\frac{2k\pi}{m}$ + i sin $\frac{2k\pi}{m}$

If m & n are co-prime then only solution is z = 1.