What are the solutions to the equation z^4-1=0 ?

The solutions to the equation z^4-1=0 are z=1,z=-1,z=i,z=-i

Find the zeros of z^4-1=0

The zeros of z^4-1=0 are z=1,z=-1,z=i,z=-i

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z^{4} - 1 = 0

z = 1, z = - 1, z = i, z = - i

Solution steps

z^{4} - 1 = 0

Move

1

to the right side

z^{4} = 1

Rewrite the equation with

u = z^{2}

and

u^{2} = z^{4}

u^{2} = 1

Solve

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

u = 1, u = - 1

Substitute back

u = z^{2},

solve for

z

Solve

z^{2} = 1 : z = 1, z = - 1

Solve

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

The solutions are

z = 1, z = - 1, z = i, z = - i

(3 x^{2} - 10 x + 8) (2 x - b) = 0

3 (t^{2} - 9)^{2} + 16 (t^{2} - 9) = - 5

D, 2 b - hb = D^{3}

x^{3} - 6 x^{2} + x - 6 = x^{2} + 1

y (y - 5)^{3} - 14 (y - 5)^{2} = 0

What are the solutions to the equation z^4-1=0 ?
The solutions to the equation z^4-1=0 are z=1,z=-1,z=i,z=-i
Find the zeros of z^4-1=0
The zeros of z^4-1=0 are z=1,z=-1,z=i,z=-i