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

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


Simplifying
z3 + (1 + -1i) * z2 + (2i + -1) * z + (i + 3) = 0

Reorder the terms for easier multiplication:
z3 + z2(1 + -1i) + (2i + -1) * z + (i + 3) = 0
z3 + (1 * z2 + -1i * z2) + (2i + -1) * z + (i + 3) = 0

Reorder the terms:
z3 + (-1iz2 + 1z2) + (2i + -1) * z + (i + 3) = 0
z3 + (-1iz2 + 1z2) + (2i + -1) * z + (i + 3) = 0

Reorder the terms:
z3 + -1iz2 + 1z2 + (-1 + 2i) * z + (i + 3) = 0

Reorder the terms for easier multiplication:
z3 + -1iz2 + 1z2 + z(-1 + 2i) + (i + 3) = 0
z3 + -1iz2 + 1z2 + (-1 * z + 2i * z) + (i + 3) = 0

Reorder the terms:
z3 + -1iz2 + 1z2 + (2iz + -1z) + (i + 3) = 0
z3 + -1iz2 + 1z2 + (2iz + -1z) + (i + 3) = 0

Reorder the terms:
z3 + -1iz2 + 1z2 + 2iz + -1z + (3 + i) = 0

Remove parenthesis around (3 + i)
z3 + -1iz2 + 1z2 + 2iz + -1z + 3 + i = 0

Reorder the terms:
3 + i + 2iz + -1iz2 + -1z + 1z2 + z3 = 0

Solving
3 + i + 2iz + -1iz2 + -1z + 1z2 + z3 = 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 + i + 2iz + -1iz2 + -1z + 1z2 + -3 + z3 = 0 + -3

Reorder the terms:
3 + -3 + i + 2iz + -1iz2 + -1z + 1z2 + z3 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + i + 2iz + -1iz2 + -1z + 1z2 + z3 = 0 + -3
i + 2iz + -1iz2 + -1z + 1z2 + z3 = 0 + -3

Combine like terms: 0 + -3 = -3
i + 2iz + -1iz2 + -1z + 1z2 + z3 = -3

Add 'z' to each side of the equation.
i + 2iz + -1iz2 + -1z + 1z2 + z + z3 = -3 + z

Reorder the terms:
i + 2iz + -1iz2 + -1z + z + 1z2 + z3 = -3 + z

Combine like terms: -1z + z = 0
i + 2iz + -1iz2 + 0 + 1z2 + z3 = -3 + z
i + 2iz + -1iz2 + 1z2 + z3 = -3 + z

Add '-1z2' to each side of the equation.
i + 2iz + -1iz2 + 1z2 + -1z2 + z3 = -3 + z + -1z2

Combine like terms: 1z2 + -1z2 = 0
i + 2iz + -1iz2 + 0 + z3 = -3 + z + -1z2
i + 2iz + -1iz2 + z3 = -3 + z + -1z2

Add '-1z3' to each side of the equation.
i + 2iz + -1iz2 + z3 + -1z3 = -3 + z + -1z2 + -1z3

Combine like terms: z3 + -1z3 = 0
i + 2iz + -1iz2 + 0 = -3 + z + -1z2 + -1z3
i + 2iz + -1iz2 = -3 + z + -1z2 + -1z3

Reorder the terms:
3 + i + 2iz + -1iz2 + -1z + z2 + z3 = -3 + z + -1z2 + -1z3 + 3 + -1z + z2 + z3

Reorder the terms:
3 + i + 2iz + -1iz2 + -1z + z2 + z3 = -3 + 3 + z + -1z + -1z2 + z2 + -1z3 + z3

Combine like terms: -3 + 3 = 0
3 + i + 2iz + -1iz2 + -1z + z2 + z3 = 0 + z + -1z + -1z2 + z2 + -1z3 + z3
3 + i + 2iz + -1iz2 + -1z + z2 + z3 = z + -1z + -1z2 + z2 + -1z3 + z3

Combine like terms: z + -1z = 0
3 + i + 2iz + -1iz2 + -1z + z2 + z3 = 0 + -1z2 + z2 + -1z3 + z3
3 + i + 2iz + -1iz2 + -1z + z2 + z3 = -1z2 + z2 + -1z3 + z3

Combine like terms: -1z2 + z2 = 0
3 + i + 2iz + -1iz2 + -1z + z2 + z3 = 0 + -1z3 + z3
3 + i + 2iz + -1iz2 + -1z + z2 + z3 = -1z3 + z3

Combine like terms: -1z3 + z3 = 0
3 + i + 2iz + -1iz2 + -1z + z2 + z3 = 0

The solution to this equation could not be determined.

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