Question

# The centre of regular polygon of n sides is located at z=0 and one of its vertices is z1. If z2 is vertex adjacent to z1, then z2=

A
z1(cos2πn±isin2πn)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
z1(cosπn±isinπn)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
z1(cosπ2n±isinπ2n)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
z1(cosπ3n±isinπ3n)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A z1(cos2πn±isin2πn)Let z1 represent a complex root of xn=an,a>0,a∈R Then each vertex of a regular n sided polygon of side length a units will represent the n roots of xn=an Also, the angle subtended by adjacent vertices at centre =2πn Let z1=aeiθ ⇒ Argument of the adjacent vertex will be θ±2πn ∴ z2=aei(θ±2πn) z2=aeiθ⋅e±2πni z2=z1(cos2πn±isin2πn)

Suggest Corrections
0
Join BYJU'S Learning Program
Select...
Related Videos
What Is a Good Fuel?
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
Select...