The Total solution for NCERT class 6-12
Find the least positive integral value of n for which [(1+i)/(1-i)]n isreal.
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.