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

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

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

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

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

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

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

Solving for variable 'i'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.