The least positive integer n for which 1+in(1-i)n-2 is a real number is

1+in(1-i)n-2=(1-i)21+i1-in=2iin=2in+1 is real if n=1,3,5..least value of n=1

The least positive integer n for which 1+in(1-i)n-2 is a real number is

1+in(1-i)n-2=(1-i)21+i1-in=2iin=2in+1 is real if n=1,3,5..least value of n=1

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The least positive integer n for which $\frac{{(1 + i)}^{n}}{{(1 - i)}^{n - 2}}$ is a real number is

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$\frac{{(1 + i)}^{n}}{{(1 - i)}^{n - 2}} = {(1 - i)}^{2} {(\frac{1 + i}{1 - i})}^{n} = 2 i {(i)}^{n} = 2 {(i)}^{n + 1} i s r e a l i f n = 1, 3, 5 . .$

least value of n=1

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The least positive integer n for which 1+in(1-i)n-2 is a real number is

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The least positive integer n for which $\frac{{(1 + i)}^{n}}{{(1 - i)}^{n - 2}}$ is a real number is