Question

Simplify the following :
If ${\left(\frac{1+i}{1-i}\right)}^x=1$ ,then for any +ive integer n, x is equal to

• A. 4n
• B. 4n + 1
• C. 2n
• D. 2n + 1

Answer 1

The correct option is A 4n

$\frac{1+i}{1-i}=\frac{\sqrt{2}{e}^{\pi i/4}}{\sqrt{2}{e}^{-\pi i/4}}=e^{\pi i/2}=Cos\frac{\pi }{2}+isin\frac{\pi }{2}=i$
$\therefore E=(i{)}^x=1.$Above is possible if x=4n where n is a +ive integer.