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

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


Simplifying
z3 + (1 + -1i) * z2 + (1 + -1i) * z + -1i = 0

Reorder the terms for easier multiplication:
z3 + z2(1 + -1i) + (1 + -1i) * z + -1i = 0
z3 + (1 * z2 + -1i * z2) + (1 + -1i) * z + -1i = 0

Reorder the terms:
z3 + (-1iz2 + 1z2) + (1 + -1i) * z + -1i = 0
z3 + (-1iz2 + 1z2) + (1 + -1i) * z + -1i = 0

Reorder the terms for easier multiplication:
z3 + -1iz2 + 1z2 + z(1 + -1i) + -1i = 0
z3 + -1iz2 + 1z2 + (1 * z + -1i * z) + -1i = 0

Reorder the terms:
z3 + -1iz2 + 1z2 + (-1iz + 1z) + -1i = 0
z3 + -1iz2 + 1z2 + (-1iz + 1z) + -1i = 0

Reorder the terms:
-1i + -1iz + -1iz2 + 1z + 1z2 + z3 = 0

Solving
-1i + -1iz + -1iz2 + 1z + 1z2 + z3 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-1z' to each side of the equation.
-1i + -1iz + -1iz2 + 1z + 1z2 + -1z + z3 = 0 + -1z

Reorder the terms:
-1i + -1iz + -1iz2 + 1z + -1z + 1z2 + z3 = 0 + -1z

Combine like terms: 1z + -1z = 0
-1i + -1iz + -1iz2 + 0 + 1z2 + z3 = 0 + -1z
-1i + -1iz + -1iz2 + 1z2 + z3 = 0 + -1z
Remove the zero:
-1i + -1iz + -1iz2 + 1z2 + z3 = -1z

Add '-1z2' to each side of the equation.
-1i + -1iz + -1iz2 + 1z2 + -1z2 + z3 = -1z + -1z2

Combine like terms: 1z2 + -1z2 = 0
-1i + -1iz + -1iz2 + 0 + z3 = -1z + -1z2
-1i + -1iz + -1iz2 + z3 = -1z + -1z2

Add '-1z3' to each side of the equation.
-1i + -1iz + -1iz2 + z3 + -1z3 = -1z + -1z2 + -1z3

Combine like terms: z3 + -1z3 = 0
-1i + -1iz + -1iz2 + 0 = -1z + -1z2 + -1z3
-1i + -1iz + -1iz2 = -1z + -1z2 + -1z3

Reorder the terms:
-1i + -1iz + -1iz2 + z + z2 + z3 = -1z + z + -1z2 + z2 + -1z3 + z3

Combine like terms: -1z + z = 0
-1i + -1iz + -1iz2 + z + z2 + z3 = 0 + -1z2 + z2 + -1z3 + z3
-1i + -1iz + -1iz2 + z + z2 + z3 = -1z2 + z2 + -1z3 + z3

Combine like terms: -1z2 + z2 = 0
-1i + -1iz + -1iz2 + z + z2 + z3 = 0 + -1z3 + z3
-1i + -1iz + -1iz2 + z + z2 + z3 = -1z3 + z3

Combine like terms: -1z3 + z3 = 0
-1i + -1iz + -1iz2 + z + z2 + z3 = 0

The solution to this equation could not be determined.

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