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Question -

Find the least positive integral value of n for which [(1+i)/(1-i)]n isreal.



Answer -

Given:

[(1+i)/(1-i)]n

Z = [(1+i)/(1-i)]n

Now let us multiplyand divide by (1+i), we get

= i [which is notreal]

For n = 2, we have

[(1+i)/(1-i)]2 =i2

= -1 [which is real]

So, the smallestpositive integral ‘n’ that can make [(1+i)/(1-i)]n real is2.

 The smallestpositive integral value of ‘n’ is 2.

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