SOLUTION: Both 2(cos 10 degrees + isin 10 degrees) and 2(cos 100 degrees + isin 100 degrees) are nth roots of a particular number. What is the smallest possible value of n?

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Question 983180: Both 2(cos 10 degrees + isin 10 degrees) and 2(cos 100 degrees + isin 100 degrees) are nth roots of a particular number. What is the smallest possible value of n?
Answer by ikleyn(52925) About Me  (Show Source):
You can put this solution on YOUR website!

Notice that  100° - 10° = 90° = pi%2F2 = 2pi%2F4.

The smallest value of  n  is  4.

Look in my lessons on complex numbers  REVIEW of lessons on complex numbers  in this site,  especially in the lesson  How to take a root of a complex number.