What are the solutions to the equation r^3=1 ?

The solutions to the equation r^3=1 are r=1,r=-1/2+(sqrt(3))/2 i,r=-1/2-(sqrt(3))/2 i

Find the zeros of r^3=1

The zeros of r^3=1 are r=1,r=-1/2+(sqrt(3))/2 i,r=-1/2-(sqrt(3))/2 i

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r^{3} = 1

r = 1, r = - \frac{1}{2} + \frac{3}{2} i, r = - \frac{1}{2} - \frac{3}{2} i

Solution steps

r^{3} = 1

For

x^{3} = f (a)

the solutions are

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

r = 1, r = \frac{- 1 + 3 i}{2}, r = \frac{- 1 - 3 i}{2}

Simplify

\frac{- 1 + 3 i}{2} : - \frac{1}{2} + \frac{3}{2} i

Simplify

\frac{- 1 - 3 i}{2} : - \frac{1}{2} - \frac{3}{2} i

r = 1, r = - \frac{1}{2} + \frac{3}{2} i, r = - \frac{1}{2} - \frac{3}{2} i

x^{3} - 13 x^{2} + 30 x = 0

x^{4} - 16 x^{2} + 32 x - 16 = 0

r^{3} - r^{2} - 4 r + 4 = 0

2 x^{3} + x^{2} - 10 x = 0

x^{4} - 5 x^{2} + 5 = 0

What are the solutions to the equation r^3=1 ?
The solutions to the equation r^3=1 are r=1,r=-1/2+(sqrt(3))/2 i,r=-1/2-(sqrt(3))/2 i
Find the zeros of r^3=1
The zeros of r^3=1 are r=1,r=-1/2+(sqrt(3))/2 i,r=-1/2-(sqrt(3))/2 i