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Properties of Iota

If α and β ar...

Question

If $α$ and $β$ are the roots of the equation $x^{2} - 2 x + 2 = 0$ , then least value of $n$ for which ${(\frac{α}{β})}^{n} = 1$ is:

A

5

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B

4

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C

3

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D

2

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Solution

The correct option is B $4$
$(x - 1)^{2} + 1 = 0 \Rightarrow x = 1 \pm i ∴ \frac{α}{β} = (\frac{1 \pm i}{1 \mp i}) = \pm (\frac{2 i}{2}) = \pm i A . T . Q {(\frac{α}{β})}^{n} = (\pm i)^{n} = 1 \Rightarrow n = 4$

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