Q24 of 153 Page 13

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.


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