the value of 10summation k=1 (sin2kpi/11 + icos2kpi/11) is(a) 1(b) -1(c) -i(d) i
Ranjita yadav , 12 Years ago
Grade 11
Magical Mathematics[Interesting Approach]> complex numbers...
2 Answers
aman mahajan
Last Activity: 12 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
Last Activity: 7 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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