Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex Numbernth roots of unityEasy2 minPYQ_2018

MathematicsEasysingle choice

The $n^{th}$ roots of unity are in

Answer:

Solution:

Let $x = 1$

$= \cos 0 ° + i \sin 0 °$

$\Rightarrow x^{1 / n} = e^{i (2 π r) / n}; r = 0, 1, 2, \dots$

Then, the roots are $1, e^{\frac{2 π i}{n}}, e^{\frac{4 π i}{n}}, \dots$ which are clearly on $GP$ with common ratio $e^{2 π i / n}$

Stream:BITSATSubject:MathematicsTopic:Complex NumberSubtopic:nth roots of unity

⏱ 2mℹ️ Source: PYQ_2018

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