Question 2 Calculate the largest integer n < o so that (1 + 3½/3 i)^n is purely imaginary.
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Well the largest integer n<0 is -1 and as it happens that gives an imaginary result.
((1+3–√)/3i)−1=3i/(1+3–√) and as 1/(1+3–√) is a Real Number it follows that this ∗3i is purely imaginary.
If you were actually thinking that -2 is a "larger" negative number, and -3 larger still then the question doesn't really make sense because any odd (negative) power of ((1+3–√)/3i) is also purely imaginary, so there would be no "largest" negative n in that sense.
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