Question

If ${\left(\frac{1+i}{1-i}\right)}^m$ = 1 then the least integral value of m is

• A. 2
• B. 4
• C. 8
• D. None of these

Answer 1

The correct option is B

4

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

∴ ${\left(\frac{1+i}{1-i}\right)}^m$ = $i^m$ = 1 (as given)

So the least value of m = 4 ( ∵ $i^4$ = 1 )