What is the small

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.