Find the smallest positive integer n for which (1 + i)2n = (1 – i)2n.


Given: (1 + i)2n = (1 – i)2n

Consider the given equation,


(1 + i)2n = (1 – i)2n




Now, rationalizing by multiply and divide by the conjugate of (1 – i)





[(a + b)2 = a2 + b2 + 2ab & (a – b)(a + b) = (a2 – b2)]


[i2 = -1]



⇒ (i)2n = 1


Now, i2n = 1 is possible if n = 2 because (i)2(2) = i4 = (-1)4 = 1


So, the smallest positive integer n = 2


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