What is the smallest positive integer n for which (1 + i)2n = (1 – i)2n?
Given:
⇒ (1+i)2n=(1-i)2n
⇒ ((1+i)2)n=((1-i)2)n
⇒ (12+i2+2(1)(i))n=(12+i2-2(1)(i))n
We know that i2=-1
⇒ (1-1+2i)n=(1-1-2i)n
⇒ (2i)n=(-2i)n
We can see that the Relation holds only when n is an even integer.
∴ The smallest positive integer n is 2.