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Question

Write the least positive integral value of n for which 1+i1-in is real.

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Solution

1+i1-in=1+i1-i×1+i1+in=1+i2+2i1-i2n=1-1+2i1+1n2i2n=inFor in to be real, the smallest positive value of n will be 2. As, i2=-1, which is real.

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