Let z = . If R(z) and I(z) respectively denote the real and imaginary parts of z, then

Engineering

Mathematics

Introduction to Complex Number

Question

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

R(z) > 0 and I(z) > 0

R(z) < 0 and I(z) > 0

R(z) = – 3

I(z) = 0

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

${(\frac{\sqrt{3}}{2} + \frac{i}{2})}^{5} = {(e^{i \frac{π}{b}})}^{5} = e^{i 5 π / 6}$

$∴ z = 2 \cos \frac{5 π}{6} = 2 (- \frac{\sqrt{3}}{2}) = - \sqrt{3}$