z^2-(1+4i)z-(5+i)=0

Solution for z^2-(1+4i)z-(5+i)=0 equation:

Simplifying
z2 + -1(1 + 4i) * z + -1(5 + i) = 0

Reorder the terms for easier multiplication:
z2 + -1z(1 + 4i) + -1(5 + i) = 0
z2 + (1 * -1z + 4i * -1z) + -1(5 + i) = 0

Reorder the terms:
z2 + (-4iz + -1z) + -1(5 + i) = 0
z2 + (-4iz + -1z) + -1(5 + i) = 0
z2 + -4iz + -1z + (5 * -1 + i * -1) = 0
z2 + -4iz + -1z + (-5 + -1i) = 0

Reorder the terms:
-5 + -1i + -4iz + -1z + z2 = 0

Solving
-5 + -1i + -4iz + -1z + z2 = 0

Solving for variable 'i'.

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

Add '5' to each side of the equation.
-5 + -1i + -4iz + -1z + 5 + z2 = 0 + 5

Reorder the terms:
-5 + 5 + -1i + -4iz + -1z + z2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1i + -4iz + -1z + z2 = 0 + 5
-1i + -4iz + -1z + z2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1i + -4iz + -1z + z2 = 5

Add 'z' to each side of the equation.
-1i + -4iz + -1z + z + z2 = 5 + z

Combine like terms: -1z + z = 0
-1i + -4iz + 0 + z2 = 5 + z
-1i + -4iz + z2 = 5 + z

Add '-1z2' to each side of the equation.
-1i + -4iz + z2 + -1z2 = 5 + z + -1z2

Combine like terms: z2 + -1z2 = 0
-1i + -4iz + 0 = 5 + z + -1z2
-1i + -4iz = 5 + z + -1z2

Reorder the terms:
-5 + -1i + -4iz + -1z + z2 = 5 + z + -1z2 + -5 + -1z + z2

Reorder the terms:
-5 + -1i + -4iz + -1z + z2 = 5 + -5 + z + -1z + -1z2 + z2

Combine like terms: 5 + -5 = 0
-5 + -1i + -4iz + -1z + z2 = 0 + z + -1z + -1z2 + z2
-5 + -1i + -4iz + -1z + z2 = z + -1z + -1z2 + z2

Combine like terms: z + -1z = 0
-5 + -1i + -4iz + -1z + z2 = 0 + -1z2 + z2
-5 + -1i + -4iz + -1z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
-5 + -1i + -4iz + -1z + z2 = 0

The solution to this equation could not be determined.