z^2+(1+4i)z+3+11i=0

Solution for z^2+(1+4i)z+3+11i=0 equation:

Simplifying
z2 + (1 + 4i) * z + 3 + 11i = 0

Reorder the terms for easier multiplication:
z2 + z(1 + 4i) + 3 + 11i = 0
z2 + (1 * z + 4i * z) + 3 + 11i = 0

Reorder the terms:
z2 + (4iz + 1z) + 3 + 11i = 0
z2 + (4iz + 1z) + 3 + 11i = 0

Reorder the terms:
3 + 11i + 4iz + 1z + z2 = 0

Solving
3 + 11i + 4iz + 1z + z2 = 0

Solving for variable 'i'.

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

Add '-3' to each side of the equation.
3 + 11i + 4iz + 1z + -3 + z2 = 0 + -3

Reorder the terms:
3 + -3 + 11i + 4iz + 1z + z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 11i + 4iz + 1z + z2 = 0 + -3
11i + 4iz + 1z + z2 = 0 + -3

Combine like terms: 0 + -3 = -3
11i + 4iz + 1z + z2 = -3

Add '-1z' to each side of the equation.
11i + 4iz + 1z + -1z + z2 = -3 + -1z

Combine like terms: 1z + -1z = 0
11i + 4iz + 0 + z2 = -3 + -1z
11i + 4iz + z2 = -3 + -1z

Add '-1z2' to each side of the equation.
11i + 4iz + z2 + -1z2 = -3 + -1z + -1z2

Combine like terms: z2 + -1z2 = 0
11i + 4iz + 0 = -3 + -1z + -1z2
11i + 4iz = -3 + -1z + -1z2

Reorder the terms:
3 + 11i + 4iz + z + z2 = -3 + -1z + -1z2 + 3 + z + z2

Reorder the terms:
3 + 11i + 4iz + z + z2 = -3 + 3 + -1z + z + -1z2 + z2

Combine like terms: -3 + 3 = 0
3 + 11i + 4iz + z + z2 = 0 + -1z + z + -1z2 + z2
3 + 11i + 4iz + z + z2 = -1z + z + -1z2 + z2

Combine like terms: -1z + z = 0
3 + 11i + 4iz + z + z2 = 0 + -1z2 + z2
3 + 11i + 4iz + z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
3 + 11i + 4iz + z + z2 = 0

The solution to this equation could not be determined.