Question

The smallest positive integer $n$ , for which ${\left(1+i\right)}^{2n}={\left(1-i\right)}^{2n}$ is

• A. $1$
• B. $2$
• C. $4$
• D. $0$

Answer 1

Answer: (B)

We have, ${\left(1+i\right)}^{2n}={\left(1-i\right)}^{2n}$
$\Rightarrow {\left(\frac{1+i}{1-i}\right)}^{2n}=1$
$\Rightarrow {\left(i\right)}^{2n}=1$ which is possible if $n=2$
$\left(\because i^4=1\right)$