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

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Solution

The correct option is B 4
$\frac{1 + i}{1 - i} = \frac{1 + i}{1 - i} \times \frac{1 + i}{1 + i} = \frac{(1 + i)^{2}}{2} = \frac{2 i}{2} = i$
${(\frac{1 + i}{1 - i})}^{m} = i^{m} = 1$ (as given)
So the least value of m = 4 $∵ i^{4} = 1$

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