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Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Easy2 minPYQ_2019

MathematicsEasysingle choice

Let $z = {(\frac{\sqrt{3}}{2} + \frac{i}{2})}^{5} + {(\frac{\sqrt{3}}{2} - \frac{i}{2})}^{5} .$ If $R (z)$ and $I (z)$ respectively denote the real and imaginary parts of $z,$ then

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Answer:

Solution:

Let $α = \frac{\sqrt{3}}{2} + \frac{i}{2},$ then $z = α^{5} + {(\bar{α})}^{5}$

We know ${\bar{z}}^{n} = {\bar{z}}^{n}$ ,

then, $z = 2 R e (α^{5})$

Hence, $I (z) = 0$ .

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

⏱ 2mℹ️ Source: PYQ_2019

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