CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

Points z1 and z2 are adjacent vertices of a regular polygon of n sides. Find the vertex z3 adjacent to z2(z3z1).

A
z2+(z2z1)[cos2πn±isin2πn].
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
z2(z1)[cos2πn±isin2πn].
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
z2+(z2z1)[sin2πn±icos2πn].
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
z2(z1)[sin2πn±icos2πn].
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A z2+(z2z1)[cos2πn±isin2πn].
Let C(z0) be the centre of the polygon and A1(z1),A3(z3) be two vertices on either side of A2(z2) as shown in figures I and II.
z1,z2 being known to be adjacent and we have to find the vertex z3 in terms of z1 and z2.
From fig. (1), rotation being anticlockwise, we have
z2z0=(z1z0)e2πi/n
z3z0=(z2z0)e2πi/n. Subtracting we get
z3z2=(z2z1)e2πi/n
z3=z2+(z2z1)e2πi/n ...(1)
Similarly, proceeding as above for the second figure in which the rotation is clockwise, we have
z3=z2+(z2z1)e2πi/n ...(2)
z3=z2+(z2z1)e±2πi/n
=z2+(z2z1)[cos2πn±isin2πn].
Ans: A
250972_191432_ans_54e7c91eb4d94cfca2e009fc29956e59.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Algebra of Continuous Functions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon