N50
z = i - 1/i + 1 = (i - 1)^2/(i-1)(i+1) = (-1 - 2i +1)/-1-1 = -2i/-2 = i
z^2006 = i^2006 = -1
N51
z = i + 1/i - 1 = (i + 1)^2/-2 = 2i/-2 = -i
z^2004 = (i)^2004 = (i^2)^1002 = (-1)^1002 = 1
N52
z = z = i + 1/i - 1 = (i + 1)^2/-2 = 2i/-2 = -i
z^2006 = (i^2)^1003 = (-1)^1003 = -1
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Answers & Comments
N50
z = i - 1/i + 1 = (i - 1)^2/(i-1)(i+1) = (-1 - 2i +1)/-1-1 = -2i/-2 = i
z^2006 = i^2006 = -1
N51
z = i + 1/i - 1 = (i + 1)^2/-2 = 2i/-2 = -i
z^2004 = (i)^2004 = (i^2)^1002 = (-1)^1002 = 1
N52
z = z = i + 1/i - 1 = (i + 1)^2/-2 = 2i/-2 = -i
z^2006 = (i^2)^1003 = (-1)^1003 = -1