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

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

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

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

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

z = - 1 + 2 i, z = - 1 - 2 i

Solution steps

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

Solve with the quadratic formula

z_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 1 \cdot 3}{2 \cdot 1}

Simplify

2^{2} - 4 \cdot 1 \cdot 3 : 22 i

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

z = - 1 + 2 i, z = - 1 - 2 i

x^{2} + 6 x + 45 = 0

- 3 x + 0 = - 4

2 x + 1 = 1

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