IIT JEE , AIEEE Forum - Mathematics , Algebra

nadeemoidu

z⁵ = 32 or -31

Let 1,z₁, z₂, z₃ ,z₄ be the fifth roots of unity.

So z= 2 , 2z₁, 2z₂, 2z₃ , 2z₄ or ⁵

(-31) , ⁵

(-31)z₁, ⁵

(-31)z₂, ⁵

(-31)z₃ , ⁵

(-31)z₄

It can be found that the arguments of the fifth roots of unity are 0, 2

/5 ,4

/5 , 6

/5 and 8

/5 .

Plot these points on the graph and the no. of negative roots can be found out.