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(52926) (Show Source): You can put this solution on YOUR website!
Notice that 100° - 10° = 90° = = .
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.
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