z^2-z-1-i=0

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

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

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

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

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

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

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

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

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

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

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

Divide each side by '-1'.
i = -1 + -1z + z2

Simplifying
i = -1 + -1z + z2