z^2+2z+(1+i)=0

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

Simplifying
z2 + 2z + (1 + i) = 0

Remove parenthesis around (1 + i)
z2 + 2z + 1 + i = 0

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

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

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

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

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

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

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

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

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

Simplifying
i = -1 + -2z + -1z2