z^2-z-1+3i=0

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

Simplifying
z2 + -1z + -1 + 3i = 0

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

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

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

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

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

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

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

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

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

Divide each side by '3'.
i = 0.3333333333 + 0.3333333333z + -0.3333333333z2

Simplifying
i = 0.3333333333 + 0.3333333333z + -0.3333333333z2