What are the solutions to the equation z^5-z=0 ?

The solutions to the equation z^5-z=0 are z=0,z=i,z=-i,z=-1,z=1

Find the zeros of z^5-z=0

The zeros of z^5-z=0 are z=0,z=i,z=-i,z=-1,z=1

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z^{5} - z = 0

z = 0, z = i, z = - i, z = - 1, z = 1

Solution steps

z^{5} - z = 0

Factor

z^{5} - z : z (z^{2} + 1) (z + 1) (z - 1)

z (z^{2} + 1) (z + 1) (z - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

z = 0 or z^{2} + 1 = 0 or z + 1 = 0 or z - 1 = 0

Solve

z^{2} + 1 = 0 : z = i, z = - i

Solve

z + 1 = 0 : z = - 1

Solve

z - 1 = 0 : z = 1

The solutions are

z = 0, z = i, z = - i, z = - 1, z = 1

1 + z^{4} = 0

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

x^{3} + 8 x^{2} + 11 x - 20 = 0

(1 + x)^{3} = 0

x^{4} - 30 x^{2} + 289 = 0

What are the solutions to the equation z^5-z=0 ?
The solutions to the equation z^5-z=0 are z=0,z=i,z=-i,z=-1,z=1
Find the zeros of z^5-z=0
The zeros of z^5-z=0 are z=0,z=i,z=-i,z=-1,z=1