Question

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

• A. $x=2n+1$
• B. $x=4n$
• C. $x=2n$
• D. $x=4n+1$, where $n\in N$

Answer 1

Answer: (B)

${\left(\frac{1+i}{1-i}\right)}^x=1$
$\Rightarrow {\left(\frac{1+i}{1-i}\times \frac{1+i}{1+i}\right)}^x=1$
$\Rightarrow {\left(i\right)}^x=1$
For $x=4n$,
$i^x=1$