The roots of the equation z 5 + z 6 + ……… z 10 = 0 where z  = 0 , 1 are represented by vertices of a pentagon having longest side length is equal d . Find d 2 .

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TestHub · Accepted Answer

d 2 = 3 . Equation reduces to z 6 = 1 ⇒ z = cos 2 k 6 π ​ + i sin 2 k 6 π ​ , k = 1 , 2 , 3 , 4 , 5 The longest side = ​ cos 3 π ​ + i sin 3 π ​ − ( cos 5 3 π ​ i sin 5 3 π ​ ) ​ = 3 ​ ​

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