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

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

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

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

Reorder the terms:
z2 + (-2iz + 1z) + -1(3 + i) = 0
z2 + (-2iz + 1z) + -1(3 + i) = 0
z2 + -2iz + 1z + (3 * -1 + i * -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 '-1z' to each side of the equation.
-1i + -2iz + 1z + -1z + z2 = 3 + -1z

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.