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

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

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

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

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

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

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

Solving for variable 'i'.

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

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

Combine like terms: 2z + -2z = 0
i + 2iz + 0 + z2 = 0 + -2z
i + 2iz + z2 = 0 + -2z
Remove the zero:
i + 2iz + z2 = -2z

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

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

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

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

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

The solution to this equation could not be determined.