Complex NumbersHard
Question
If A1, A2, ...., An be the vertices of an n-sided regular polygon such that 
, then find the value of n
, then find the value of nOptions
A.5
B.7
C.8
D.9
Solution
Let centre be origin & A1 be Z0 & OA1 = OA2 = .... = a
So A2 = z0
, A3 = z0 
......
Now A1 A2 =
= | z0| 
= 2a sin 
similarlly A1 A3 = 2a sin
, A1A4 = 2a sin
Given
⇒ sin
⇒ 
⇒ n = 7 is only possible value.
So A2 = z0
, A3 = z0 ......Now A1 A2 =
= | z0| = 2a sin similarlly A1 A3 = 2a sin
, A1A4 = 2a sin Given
⇒ sin
⇒ ⇒ n = 7 is only possible value.
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