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can you plz give idea abt the concept of cube roots of unity

can you plz give idea abt the concept of cube roots of unity

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2 Answers

kawaljeet kumar
34 Points
11 years ago

consider:

           i^m/n  has n number of roots 

so  z = 1^1/3 has 3 roots.

It can also be written as        z^3 - 1 =0 this is a cubic equation just as a quadratic one so roots of this cubic quation gives

the cube roots of unity.

    1 = cos0 + isin0 =cos2k(pie) + isin2k(pie) 

   1^1/3 =e^i2kpie/3                where k = 0, 1, 2 

 

so roots are :-   1,  e^i2pie/3, e^i4pie/3

 

Manash nath
29 Points
11 years ago

let z be a cube root of 1

=>z3 =1

=>z3 -1 =0

=>(z-1)(z2+z+1) =0

=>z=1 or z2+z+1=0

so the cube roots of unity are 1 and two conjugate complex nos.

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