Complex NumbersHard

Question

The value of is

Options

A.-1

B.0

C.- i

D.i

Solution

= - i{e^i2π/7 + e^i4π/7 + e^i6π/7 + e^i8π/7 + e^i10π/7 + e^i12π/7}

, (∵ e^i14π/7 = 7)

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