    Question

# If z1 and ¯z2 represent adjacent vertices of a regular polygon of n sides and if Im(z1)Re(z1)=√2−1, Then n is equal to

A
8
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
16
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
18
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
24
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A 8Since z1 and ¯z2 are the adjacent vertices of a regular polygon of n sides, we have ∠ z10¯z1=2πn and ∣ z1∣=∣¯z1∣. Thus, z1=¯z1e2π i/n Let z1=r(cosθ+i sin θ)=reiθ ⇒ ¯z1=re−iθ since z1=¯z2π i/n1 ⇒ reiθ=re−iθe2π i/n=re2π i/n−iθ ⇒ θ=2πn−θ−θ or θ=πn Therefore z1=r(cosθ+i sin θ)=r[cos(πn)+i sin(πn)] Now,Im(z1)Re(z1)=√2−1⇒rsin(πn)rcos(πn)=√2−1 ⇒ tan(πn)=√2−1=tanπ8 ⇒ n=8  Suggest Corrections  3      Similar questions
Join BYJU'S Learning Program
Select...  Related Videos   What Is a Good Fuel?
MATHEMATICS
Watch in App  Explore more
Join BYJU'S Learning Program
Select...