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Q.

If ${(\frac{1 + i}{1 - i})}^{n} = 1$ , then the least positive integral value of $n$ is

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a

2

b

none of these

c

3

d

4

answer is C.

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Detailed Solution

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

$= \frac{1 + i^{2} + 2 i}{1^{2} + 1^{2}} = i$

$\Rightarrow {(\frac{1 + i}{1 - i})}^{n} = 1$

$\Rightarrow i^{n} = 1$

$\Rightarrow n = 4$

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