Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Medium2 minPYQ_2019

MathematicsMediumsingle choice

If $z_{1}$ and ${\bar{z}}_{1}$ represents adjacent vertices of a regular polygon of $n$ sides and if $\frac{I m (z_{1})}{R e (z_{1})} = \sqrt{2} - 1$ , then $n$ is equal to

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Answer:

Solution:

Let $z_{1} = r e^{i θ}$

then, ${\bar{z}}_{1} = r e^{- i θ}$

$\frac{z_{1}}{{\bar{z}}_{1}} = e^{2 i θ} = e^{2 π i / n}$

$\Rightarrow θ = \frac{π}{n}$

Also, $\frac{I_{m} (z_{1})}{R_{e} (z_{1})} = \tan θ = \tan \frac{π}{n} = \sqrt{2} - 1$

$\Rightarrow \tan \frac{π}{8} = \sqrt{2} - 1$

$∴ n = 8$

Stream:BITSATSubject:MathematicsTopic:Complex NumberSubtopic:General(Modulus,Argument,Conjugate)

⏱ 2mℹ️ Source: PYQ_2019

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