z^2+2z+1+8i=0

Solution for z^2+2z+1+8i=0 equation:

Simplifying
z2 + 2z + 1 + 8i = 0

Reorder the terms:
1 + 8i + 2z + z2 = 0

Solving
1 + 8i + 2z + z2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + 8i + 2z + -1 + z2 = 0 + -1

Reorder the terms:
1 + -1 + 8i + 2z + z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8i + 2z + z2 = 0 + -1
8i + 2z + z2 = 0 + -1

Combine like terms: 0 + -1 = -1
8i + 2z + z2 = -1

Add '-2z' to each side of the equation.
8i + 2z + -2z + z2 = -1 + -2z

Combine like terms: 2z + -2z = 0
8i + 0 + z2 = -1 + -2z
8i + z2 = -1 + -2z

Add '-1z2' to each side of the equation.
8i + z2 + -1z2 = -1 + -2z + -1z2

Combine like terms: z2 + -1z2 = 0
8i + 0 = -1 + -2z + -1z2
8i = -1 + -2z + -1z2

Divide each side by '8'.
i = -0.125 + -0.25z + -0.125z2

Simplifying
i = -0.125 + -0.25z + -0.125z2