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

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

Find the zeros of z^3=1

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

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z^{3} = 1

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

Solution steps

z^{3} = 1

For

x^{3} = f (a)

the solutions are

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

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

x^{3} - 4 x = 0

2 x^{3} - 8 x^{2} - 8 x + 32 = 0

x^{3} - x + 1 x = \frac{2}{3}

x^{3} + x^{2} + x + 1 = 0

a = (x^{3} + 1) (x^{6} - x^{3} + 1)

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