z^2-(3+i)z+(2+2i)=0

Solution for z^2-(3+i)z+(2+2i)=0 equation:

Simplifying
z2 + -1(3 + i) * z + (2 + 2i) = 0

Reorder the terms for easier multiplication:
z2 + -1z(3 + i) + (2 + 2i) = 0
z2 + (3 * -1z + i * -1z) + (2 + 2i) = 0

Reorder the terms:
z2 + (-1iz + -3z) + (2 + 2i) = 0
z2 + (-1iz + -3z) + (2 + 2i) = 0

Remove parenthesis around (2 + 2i)
z2 + -1iz + -3z + 2 + 2i = 0

Reorder the terms:
2 + 2i + -1iz + -3z + z2 = 0

Solving
2 + 2i + -1iz + -3z + z2 = 0

Solving for variable 'i'.

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

Add '-2' to each side of the equation.
2 + 2i + -1iz + -3z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + 2i + -1iz + -3z + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2i + -1iz + -3z + z2 = 0 + -2
2i + -1iz + -3z + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
2i + -1iz + -3z + z2 = -2

Add '3z' to each side of the equation.
2i + -1iz + -3z + 3z + z2 = -2 + 3z

Combine like terms: -3z + 3z = 0
2i + -1iz + 0 + z2 = -2 + 3z
2i + -1iz + z2 = -2 + 3z

Add '-1z2' to each side of the equation.
2i + -1iz + z2 + -1z2 = -2 + 3z + -1z2

Combine like terms: z2 + -1z2 = 0
2i + -1iz + 0 = -2 + 3z + -1z2
2i + -1iz = -2 + 3z + -1z2

Reorder the terms:
2 + 2i + -1iz + -3z + z2 = -2 + 3z + -1z2 + 2 + -3z + z2

Reorder the terms:
2 + 2i + -1iz + -3z + z2 = -2 + 2 + 3z + -3z + -1z2 + z2

Combine like terms: -2 + 2 = 0
2 + 2i + -1iz + -3z + z2 = 0 + 3z + -3z + -1z2 + z2
2 + 2i + -1iz + -3z + z2 = 3z + -3z + -1z2 + z2

Combine like terms: 3z + -3z = 0
2 + 2i + -1iz + -3z + z2 = 0 + -1z2 + z2
2 + 2i + -1iz + -3z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
2 + 2i + -1iz + -3z + z2 = 0

The solution to this equation could not be determined.