Find the least positive integral value of n for which (1+i/1-i)n is real.
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rationalize by (1+i/1+i)^n
then you will get
(1-1+2i)/(2)^n
= (2i/2)^n
= (i)^n
so
i^2=-1
but i^4=1
hence least positive integral value for n is 4.
then you will get
(1-1+2i)/(2)^n
= (2i/2)^n
= (i)^n
so
i^2=-1
but i^4=1
hence least positive integral value for n is 4.
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