The least positive integer n such that ( 2 i ) n ( 1 - i ) n - 2 , i = - 1 , is a positive integer, is ______.

The least positive integer n such that (2i)n(1-i)n-2,i=-1, is a positive integer, is ______.

Solution

(2i)n(1-i)n-2

=(2i)n(-2i)n-22

=(2i)n+22(-1)n-22

=2n+22in+22(-1)n-22
Clearly n must be even n=2,4 rejected. 

So the least positive integer possible is n=6

Asked in: JEE Main 2021 (26 Aug Shift 2)

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