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

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

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

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

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w^{2} + w + 1 = 0

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

Solution steps

w^{2} + w + 1 = 0

Solve with the quadratic formula

w_{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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

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

x, x^{2} + y^{2} = c x

x^{2} + x - 6

x^{2} + 2 = 102

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

15 + 4 x - 2 x^{2} = 0

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