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If (sqrt(3) - i)ⁿ = 2ⁿ for some integer n, then n must be a multiple of which number?

1. 6
2. 10
3. 9
4. 12

Correct answer: 12

Solution

In polar form the argument is -n*pi/6; for the result to equal 2ⁿ (a positive real), -n*pi/6 must be a multiple of 2*pi, forcing n to be a multiple of 12.

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