106incentre is the centre of the circle which is inscribed inside the polygon.
thinking about the question
Let z_i be in G.P for all i satisfying 1≤i≤n and 1st term is unity.
Also z1+z2+z3+....zn=0
Now if z1,z2,z3....znrepresent vertices of a n-sided polygon, find the distance bet circum-centre and incentre of the polygon.
P.S - What s the incentre of a polygon?
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8 Answers
106
106Why ?? it is not mentioned that the polygon is regular.. the complex nos might have different values of magnitude.. (perhaps)
1yes answer is 0
Z1,Z2,Z3,...............,Zn=1,r,r2,r3,...........rn-1
where r is complex
z1+z2+z3+......................zn=0
or (rn-1/r-1)=0
r≠1
thus rn=1
thus z1,z2 ,z3...............zn are the n nth roots of unity
hence they form a regular polygon with boyh incentre and circumcentre at the origin.
hence ans is 0.
11I don't know what they mean by saying complex nos. are in GP......
BTW this was a MCQ.....options were :-
a) \sqrt{cot\frac{2\pi}{n}-cos\frac{2\pi}{n}}
b) 2
c) \frac{1}{2}
d) NOT