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

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

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

Reorder the terms for easier multiplication:
z2 + z(1 + 2i) + 1 + i = 0
z2 + (1 * z + 2i * z) + 1 + i = 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.