MCQ
The smallest positive integer $n$ for which $(1+i)^{2 n}=(1-i)^{2 n}$ is
  • A
    1
  • 2
  • C
    3
  • D
    4

Answer

Correct option: B.
2
(B)
We have, $(1+i)^{2 n}=(1-i)^{2 n}$
$\Rightarrow\left(\frac{1+ i }{1- i }\right)^{2 n }=1 \Rightarrow( i )^{2 n }=1$
$\Rightarrow( i )^{2 n }=(-1)^2 \Rightarrow( i )^{2 n }=\left( i ^2\right)^2$
$\Rightarrow( i )^{2 n }=( i )^4 \Rightarrow 2 n =4$
$\Rightarrow n =2$

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