Question

If ${\left(\frac{1+i}{1-i}\right)}^m=1,$ then the least integral value of m is
[IIT 1982; MNR 1984; UPSEAT 2001; MP PET 2002]

• 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 $\because i^4=1$