What are the solutions to the equation roots x^4+1 ?

The solutions to the equation roots x^4+1 are

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roots x^4+1

roots

x^{4} + 1

x = \frac{1}{2} + \frac{1}{2} i, x = - \frac{1}{2} - \frac{1}{2} i, x = \frac{1}{2} - \frac{1}{2} i, x = - \frac{1}{2} + \frac{1}{2} i

Solution steps

x^{4} + 1

The roots are the intercepts with the x-axis

(y = 0)

x^{4} + 1 = 0

Move

1

to the right side

x^{4} = - 1

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} = - 1

Solve

u^{2} = - 1 : u = i, u = - i

u = i, u = - i

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = i : x = \frac{1}{2} + \frac{1}{2} i, x = - \frac{1}{2} - \frac{1}{2} i

Solve

x^{2} = - i : x = \frac{1}{2} - \frac{1}{2} i, x = - \frac{1}{2} + \frac{1}{2} i

The solutions are

x = \frac{1}{2} + \frac{1}{2} i, x = - \frac{1}{2} - \frac{1}{2} i, x = \frac{1}{2} - \frac{1}{2} i, x = - \frac{1}{2} + \frac{1}{2} i

60 x^{3} - 360 x^{2} = 0

x^{11} = 3

z^{4} = - 7 + 24 i

x^{6} - 81 x^{2} = 0

4 x^{3} - 9 x^{2} + 6 x = 0

What are the solutions to the equation roots x^4+1 ?
The solutions to the equation roots x^4+1 are
Find the zeros of roots x^4+1
The zeros of roots x^4+1 are