Find the least positive integral value of n for which ( 1+i/1-i ) ^n is real.


Let us assume the given complex number be


Multiplying and dividing with 1+i


⇒


⇒


We know that i2=-1


⇒


⇒


⇒


⇒


We know that i2k is real for k>0.


So, the smallest positive integral ‘n’ that can make real is 2.


∴ The smallest positive integral value of ‘n’ is 2.


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