The value of 2Π6p=1(sin2pπ7−icos2pπ7) is
y=2Π6p=1(sin2pπ7−icos2pπ7)iy=2Π6p=1(isin2pπ7−i2cos2pπ7)iy=2Π6p=1(cos2pπ7+isin2pπ7)iy=2e∑6p=1i⎛⎝2pπ7⎞⎠iy=2e2πi7∑6p=1piy=2e2πi7×21=ei6πiy=2(cos6π+isin6π)iy=2i2y=2iy=−2i
So, option B is correct.