z^2-(3+4i)z+5i-1=0

Solution for z^2-(3+4i)z+5i-1=0 equation:

Simplifying
z2 + -1(3 + 4i) * z + 5i + -1 = 0

Reorder the terms for easier multiplication:
z2 + -1z(3 + 4i) + 5i + -1 = 0
z2 + (3 * -1z + 4i * -1z) + 5i + -1 = 0

Reorder the terms:
z2 + (-4iz + -3z) + 5i + -1 = 0
z2 + (-4iz + -3z) + 5i + -1 = 0

Reorder the terms:
-1 + 5i + -4iz + -3z + z2 = 0

Solving
-1 + 5i + -4iz + -3z + 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 + -4iz + -3z + 1 + z2 = 0 + 1

Reorder the terms:
-1 + 1 + 5i + -4iz + -3z + z2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 5i + -4iz + -3z + z2 = 0 + 1
5i + -4iz + -3z + z2 = 0 + 1

Combine like terms: 0 + 1 = 1
5i + -4iz + -3z + z2 = 1

Add '3z' to each side of the equation.
5i + -4iz + -3z + 3z + z2 = 1 + 3z

Combine like terms: -3z + 3z = 0
5i + -4iz + 0 + z2 = 1 + 3z
5i + -4iz + z2 = 1 + 3z

Add '-1z2' to each side of the equation.
5i + -4iz + z2 + -1z2 = 1 + 3z + -1z2

Combine like terms: z2 + -1z2 = 0
5i + -4iz + 0 = 1 + 3z + -1z2
5i + -4iz = 1 + 3z + -1z2

Reorder the terms:
-1 + 5i + -4iz + -3z + z2 = 1 + 3z + -1z2 + -1 + -3z + z2

Reorder the terms:
-1 + 5i + -4iz + -3z + z2 = 1 + -1 + 3z + -3z + -1z2 + z2

Combine like terms: 1 + -1 = 0
-1 + 5i + -4iz + -3z + z2 = 0 + 3z + -3z + -1z2 + z2
-1 + 5i + -4iz + -3z + z2 = 3z + -3z + -1z2 + z2

Combine like terms: 3z + -3z = 0
-1 + 5i + -4iz + -3z + z2 = 0 + -1z2 + z2
-1 + 5i + -4iz + -3z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
-1 + 5i + -4iz + -3z + z2 = 0

The solution to this equation could not be determined.