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Grade 11Magical Mathematics[Interesting Approach]

the value of 10summation k=1 (sin2kpi/11 + icos2kpi/11) is

(a) 1 (b) -1

(c) -i (d) i

Ranjita yadav

14 Years agoGrade 11

2 Answers

aman mahajan

14 Years ago

ans:(d)

Let S be the sum of the series from k=1 to k=10

Also we know that sum of 11th roots of unity=0.

This implies that S+sinpi+icospi=0

Hence S=i

souryadeep

9 Years ago

Take i common …... that will make it cos 2kpi/11- isin 2kpi/11 which are roots of z to the power 11 =-1........

the sum therefore is total sum of roots(which is zero) except -1 . Hence the ans is 1*i=i.....(d) ;)

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