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

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

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

The zeros of z^2+z+1=0 are z=-1/2+i(sqrt(3))/2 ,z=-1/2-i(sqrt(3))/2

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z^{2} + z + 1 = 0

z = - \frac{1}{2} + i \frac{3}{2}, z = - \frac{1}{2} - i \frac{3}{2}

Solution steps

z^{2} + z + 1 = 0

Solve with the quadratic formula

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

Simplify

1^{2} - 4 \cdot 1 \cdot 1 : 3 i

z_{1, 2} = \frac{- 1 \pm 3 i}{2 \cdot 1}

Separate the solutions

z_{1} = \frac{- 1 + 3 i}{2 \cdot 1}, z_{2} = \frac{- 1 - 3 i}{2 \cdot 1}

z = \frac{- 1 + 3 i}{2 \cdot 1} : - \frac{1}{2} + i \frac{3}{2}

z = \frac{- 1 - 3 i}{2 \cdot 1} : - \frac{1}{2} - i \frac{3}{2}

The solutions to the quadratic equation are:

z = - \frac{1}{2} + i \frac{3}{2}, z = - \frac{1}{2} - i \frac{3}{2}

7 x = 54 + x

- 16 + k = - 11

2 x^{2} - 13 x - 24

5 x - 7 = - 12

- 10 x + 5 = - 6 x - 35

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