z^2+(1+3i)z+(4+19i)=0

Solution for z^2+(1+3i)z+(4+19i)=0 equation:

Simplifying
z2 + (1 + 3i) * z + (4 + 19i) = 0

Reorder the terms for easier multiplication:
z2 + z(1 + 3i) + (4 + 19i) = 0
z2 + (1 * z + 3i * z) + (4 + 19i) = 0

Reorder the terms:
z2 + (3iz + 1z) + (4 + 19i) = 0
z2 + (3iz + 1z) + (4 + 19i) = 0

Remove parenthesis around (4 + 19i)
z2 + 3iz + 1z + 4 + 19i = 0

Reorder the terms:
4 + 19i + 3iz + 1z + z2 = 0

Solving
4 + 19i + 3iz + 1z + z2 = 0

Solving for variable 'i'.

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

Add '-4' to each side of the equation.
4 + 19i + 3iz + 1z + -4 + z2 = 0 + -4

Reorder the terms:
4 + -4 + 19i + 3iz + 1z + z2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 19i + 3iz + 1z + z2 = 0 + -4
19i + 3iz + 1z + z2 = 0 + -4

Combine like terms: 0 + -4 = -4
19i + 3iz + 1z + z2 = -4

Add '-1z' to each side of the equation.
19i + 3iz + 1z + -1z + z2 = -4 + -1z

Combine like terms: 1z + -1z = 0
19i + 3iz + 0 + z2 = -4 + -1z
19i + 3iz + z2 = -4 + -1z

Add '-1z2' to each side of the equation.
19i + 3iz + z2 + -1z2 = -4 + -1z + -1z2

Combine like terms: z2 + -1z2 = 0
19i + 3iz + 0 = -4 + -1z + -1z2
19i + 3iz = -4 + -1z + -1z2

Reorder the terms:
4 + 19i + 3iz + z + z2 = -4 + -1z + -1z2 + 4 + z + z2

Reorder the terms:
4 + 19i + 3iz + z + z2 = -4 + 4 + -1z + z + -1z2 + z2

Combine like terms: -4 + 4 = 0
4 + 19i + 3iz + z + z2 = 0 + -1z + z + -1z2 + z2
4 + 19i + 3iz + z + z2 = -1z + z + -1z2 + z2

Combine like terms: -1z + z = 0
4 + 19i + 3iz + z + z2 = 0 + -1z2 + z2
4 + 19i + 3iz + z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
4 + 19i + 3iz + z + z2 = 0

The solution to this equation could not be determined.