z^2-(1-2i)z+(1+5i)=0

Solution for z^2-(1-2i)z+(1+5i)=0 equation:

Simplifying
z2 + -1(1 + -2i) * z + (1 + 5i) = 0

Reorder the terms for easier multiplication:
z2 + -1z(1 + -2i) + (1 + 5i) = 0
z2 + (1 * -1z + -2i * -1z) + (1 + 5i) = 0

Reorder the terms:
z2 + (2iz + -1z) + (1 + 5i) = 0
z2 + (2iz + -1z) + (1 + 5i) = 0

Remove parenthesis around (1 + 5i)
z2 + 2iz + -1z + 1 + 5i = 0

Reorder the terms:
1 + 5i + 2iz + -1z + z2 = 0

Solving
1 + 5i + 2iz + -1z + 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 + 5i + 2iz + -1z + -1 + z2 = 0 + -1

Reorder the terms:
1 + -1 + 5i + 2iz + -1z + z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5i + 2iz + -1z + z2 = 0 + -1
5i + 2iz + -1z + z2 = 0 + -1

Combine like terms: 0 + -1 = -1
5i + 2iz + -1z + z2 = -1

Add 'z' to each side of the equation.
5i + 2iz + -1z + z + z2 = -1 + z

Combine like terms: -1z + z = 0
5i + 2iz + 0 + z2 = -1 + z
5i + 2iz + z2 = -1 + z

Add '-1z2' to each side of the equation.
5i + 2iz + z2 + -1z2 = -1 + z + -1z2

Combine like terms: z2 + -1z2 = 0
5i + 2iz + 0 = -1 + z + -1z2
5i + 2iz = -1 + z + -1z2

Reorder the terms:
1 + 5i + 2iz + -1z + z2 = -1 + z + -1z2 + 1 + -1z + z2

Reorder the terms:
1 + 5i + 2iz + -1z + z2 = -1 + 1 + z + -1z + -1z2 + z2

Combine like terms: -1 + 1 = 0
1 + 5i + 2iz + -1z + z2 = 0 + z + -1z + -1z2 + z2
1 + 5i + 2iz + -1z + z2 = z + -1z + -1z2 + z2

Combine like terms: z + -1z = 0
1 + 5i + 2iz + -1z + z2 = 0 + -1z2 + z2
1 + 5i + 2iz + -1z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
1 + 5i + 2iz + -1z + z2 = 0

The solution to this equation could not be determined.