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If $\left(\dfrac{1+i}{1-i}\right)^{x}=1$, then

1) $x=4 n$, where $n$ is any positive integer
2) $x=2 n$, where $n$ is any positive integer
3) $x=4 n+1$, where $n$ is any positive integer
4) $x=2 n+1$, where $n$ is any positive integer
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(1)

Explanation

$\dfrac{1+i}{1-i}=\frac{(1+i)^{2}}{2}=i$

$\left(\dfrac{1+i}{1-i}\right)^{x}=i^{x} \Rightarrow x=4 n$

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