Solve (n^2+n+1)^2

Evaluate

(n^{2} + n + 1)^{2}

To find the roots of the expression,set the expression equal to 0

(n^{2} + n + 1)^{2} = 0

The only way a power can be 0 is when the base equals 0

n^{2} + n + 1 = 0

Substitute a= 1,b= 1 and c= 1 into the quadratic formula n = \frac{- b \pm b ^{2} - 4 a c}{2 a}

n = \frac{- 1 \pm 1 ^{2} - 4}{2}

Simplify the expression

More Steps

n = \frac{- 1 \pm - 3}{2}

Simplify the radical expression

More Steps

n = \frac{- 1 \pm 3 \times i}{2}

Separate the equation into 2 possible cases

n = \frac{- 1 + 3 \times i}{2} n = \frac{- 1 - 3 \times i}{2}

Simplify the expression

More Steps

n = - \frac{1}{2} + \frac{3}{2} i n = \frac{- 1 - 3 \times i}{2}

Simplify the expression

More Steps

n = - \frac{1}{2} + \frac{3}{2} i n = - \frac{1}{2} - \frac{3}{2} i

Solution

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

Alternative Form

n_{1} \approx - 0.5 - 0.866025 i, n_{2} \approx - 0.5 + 0.866025 i

Simplify the expression