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

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

Simplifying
z2 + -1(1 + 2i) * z + -1(3 + -1i) = 0

Reorder the terms for easier multiplication:
z2 + -1z(1 + 2i) + -1(3 + -1i) = 0
z2 + (1 * -1z + 2i * -1z) + -1(3 + -1i) = 0

Reorder the terms:
z2 + (-2iz + -1z) + -1(3 + -1i) = 0
z2 + (-2iz + -1z) + -1(3 + -1i) = 0
z2 + -2iz + -1z + (3 * -1 + -1i * -1) = 0
z2 + -2iz + -1z + (-3 + 1i) = 0

Reorder the terms:
-3 + 1i + -2iz + -1z + z2 = 0

Solving
-3 + 1i + -2iz + -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 + 1i + -2iz + -1z + 3 + z2 = 0 + 3

Reorder the terms:
-3 + 3 + 1i + -2iz + -1z + z2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 1i + -2iz + -1z + z2 = 0 + 3
1i + -2iz + -1z + z2 = 0 + 3

Combine like terms: 0 + 3 = 3
1i + -2iz + -1z + z2 = 3

Add 'z' to each side of the equation.
1i + -2iz + -1z + z + z2 = 3 + z

Combine like terms: -1z + z = 0
1i + -2iz + 0 + z2 = 3 + z
1i + -2iz + z2 = 3 + z

Add '-1z2' to each side of the equation.
1i + -2iz + z2 + -1z2 = 3 + z + -1z2

Combine like terms: z2 + -1z2 = 0
1i + -2iz + 0 = 3 + z + -1z2
1i + -2iz = 3 + z + -1z2

Reorder the terms:
-3 + 1i + -2iz + -1z + z2 = 3 + z + -1z2 + -3 + -1z + z2

Reorder the terms:
-3 + 1i + -2iz + -1z + z2 = 3 + -3 + z + -1z + -1z2 + z2

Combine like terms: 3 + -3 = 0
-3 + 1i + -2iz + -1z + z2 = 0 + z + -1z + -1z2 + z2
-3 + 1i + -2iz + -1z + z2 = z + -1z + -1z2 + z2

Combine like terms: z + -1z = 0
-3 + 1i + -2iz + -1z + z2 = 0 + -1z2 + z2
-3 + 1i + -2iz + -1z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
-3 + 1i + -2iz + -1z + z2 = 0

The solution to this equation could not be determined.