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

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

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

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

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

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

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

Solving for variable 'i'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.