What are the solutions to the equation 1-z+z^2-z^3=0 ?

The solutions to the equation 1-z+z^2-z^3=0 are z=1,z=i,z=-i

Find the zeros of 1-z+z^2-z^3=0

The zeros of 1-z+z^2-z^3=0 are z=1,z=i,z=-i

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1 - z + z^{2} - z^{3} = 0

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

Solution steps

1 - z + z^{2} - z^{3} = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- z^{3} + z^{2} - z + 1 = 0

Factor

- z^{3} + z^{2} - z + 1 : - (z - 1) (z^{2} + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

z - 1 = 0 : z = 1

Solve

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

The solutions are

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

50 + 2 (\frac{x - 2}{4})^{3} = 300

z^{3} = \frac{1}{8 i}

x^{3} - 8 x^{2} + 4 x = 32

x^{6} + 3 x^{3} - 5 = 0

2 y^{4} - 9 y^{3} + 14 y^{2} + 6 y - 63 = 0

What are the solutions to the equation 1-z+z^2-z^3=0 ?
The solutions to the equation 1-z+z^2-z^3=0 are z=1,z=i,z=-i
Find the zeros of 1-z+z^2-z^3=0
The zeros of 1-z+z^2-z^3=0 are z=1,z=i,z=-i