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Question

Write the least positive integeral vlaue of n for which (1+i1i)n is real.


Solution

For n = 1

(1+i1i)1=1+i1i=1+i1i×1+i1+i=(1+i)212+12=12+i2+2i2=11+2i2=2i2=iFor n = 2(1+i1i)2=(i)2=1, which is real

Hence least positive integral value of n is 2.

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