What are the solutions to the equation z^2=z ?

The solutions to the equation z^2=z are z=1,z=0

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z^2=z

z^{2} = z

z = 1, z = 0

Solution steps

z^{2} = z

Move

z

to the left side

z^{2} - z = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 1 \cdot 0}{2 \cdot 1}

(- 1)^{2} - 4 \cdot 1 \cdot 0 = 1

z_{1, 2} = \frac{- ( - 1 ) \pm 1}{2 \cdot 1}

Separate the solutions

z_{1} = \frac{- ( - 1 ) + 1}{2 \cdot 1}, z_{2} = \frac{- ( - 1 ) - 1}{2 \cdot 1}

z = \frac{- ( - 1 ) + 1}{2 \cdot 1} : 1

z = \frac{- ( - 1 ) - 1}{2 \cdot 1} : 0

The solutions to the quadratic equation are:

z = 1, z = 0

x, f = x^{2} + m x + n

(x + 1)^{2} = 49

16 x^{2} - 32 x + 16 = 1

a^{2} + 2 a - 1 = 0

x^{2} + 2 x - 7 = 17

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