Q. 24

# What is the smallest positive integer n for which (1 + i)^{2n} = (1 – i)^{2n}?

Answer :

Given:

⇒ (1+i)^{2n}=(1-i)^{2n}

⇒ ((1+i)^{2})^{n}=((1-i)^{2})^{n}

⇒ (1^{2}+i^{2}+2(1)(i))^{n}=(1^{2}+i^{2}-2(1)(i))^{n}

We know that i^{2}=-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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