z^2+2(1+2i)z-(11+2i)=0

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

Simplifying
z2 + 2(1 + 2i) * z + -1(11 + 2i) = 0

Reorder the terms for easier multiplication:
z2 + 2z(1 + 2i) + -1(11 + 2i) = 0
z2 + (1 * 2z + 2i * 2z) + -1(11 + 2i) = 0

Reorder the terms:
z2 + (4iz + 2z) + -1(11 + 2i) = 0
z2 + (4iz + 2z) + -1(11 + 2i) = 0
z2 + 4iz + 2z + (11 * -1 + 2i * -1) = 0
z2 + 4iz + 2z + (-11 + -2i) = 0

Reorder the terms:
-11 + -2i + 4iz + 2z + z2 = 0

Solving
-11 + -2i + 4iz + 2z + z2 = 0

Solving for variable 'i'.

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

Add '11' to each side of the equation.
-11 + -2i + 4iz + 2z + 11 + z2 = 0 + 11

Reorder the terms:
-11 + 11 + -2i + 4iz + 2z + z2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2i + 4iz + 2z + z2 = 0 + 11
-2i + 4iz + 2z + z2 = 0 + 11

Combine like terms: 0 + 11 = 11
-2i + 4iz + 2z + z2 = 11

Add '-2z' to each side of the equation.
-2i + 4iz + 2z + -2z + z2 = 11 + -2z

Combine like terms: 2z + -2z = 0
-2i + 4iz + 0 + z2 = 11 + -2z
-2i + 4iz + z2 = 11 + -2z

Add '-1z2' to each side of the equation.
-2i + 4iz + z2 + -1z2 = 11 + -2z + -1z2

Combine like terms: z2 + -1z2 = 0
-2i + 4iz + 0 = 11 + -2z + -1z2
-2i + 4iz = 11 + -2z + -1z2

Reorder the terms:
-11 + -2i + 4iz + 2z + z2 = 11 + -2z + -1z2 + -11 + 2z + z2

Reorder the terms:
-11 + -2i + 4iz + 2z + z2 = 11 + -11 + -2z + 2z + -1z2 + z2

Combine like terms: 11 + -11 = 0
-11 + -2i + 4iz + 2z + z2 = 0 + -2z + 2z + -1z2 + z2
-11 + -2i + 4iz + 2z + z2 = -2z + 2z + -1z2 + z2

Combine like terms: -2z + 2z = 0
-11 + -2i + 4iz + 2z + z2 = 0 + -1z2 + z2
-11 + -2i + 4iz + 2z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
-11 + -2i + 4iz + 2z + z2 = 0

The solution to this equation could not be determined.