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

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

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

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

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

Reorder the terms:
z2 + (iz + -1z) + -1 = 0
z2 + (iz + -1z) + -1 = 0

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

Solving
-1 + iz + -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 + iz + -1z + 1 + z2 = 0 + 1

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

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

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

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

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

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

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

Divide each side by 'z'.
i = z-1 + 1 + -1z

Simplifying
i = z-1 + 1 + -1z

Reorder the terms:
i = 1 + z-1 + -1z