z^6-(3+i)z^3+2+2i=0

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Solution for z^6-(3+i)z^3+2+2i=0 equation: 


Simplifying
z6 + -1(3 + i) * z3 + 2 + 2i = 0

Reorder the terms for easier multiplication:
z6 + -1z3(3 + i) + 2 + 2i = 0
z6 + (3 * -1z3 + i * -1z3) + 2 + 2i = 0

Reorder the terms:
z6 + (-1iz3 + -3z3) + 2 + 2i = 0
z6 + (-1iz3 + -3z3) + 2 + 2i = 0

Reorder the terms:
2 + 2i + -1iz3 + -3z3 + z6 = 0

Solving
2 + 2i + -1iz3 + -3z3 + z6 = 0

Solving for variable 'i'.

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

Add '-2' to each side of the equation.
2 + 2i + -1iz3 + -3z3 + -2 + z6 = 0 + -2

Reorder the terms:
2 + -2 + 2i + -1iz3 + -3z3 + z6 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2i + -1iz3 + -3z3 + z6 = 0 + -2
2i + -1iz3 + -3z3 + z6 = 0 + -2

Combine like terms: 0 + -2 = -2
2i + -1iz3 + -3z3 + z6 = -2

Add '3z3' to each side of the equation.
2i + -1iz3 + -3z3 + 3z3 + z6 = -2 + 3z3

Combine like terms: -3z3 + 3z3 = 0
2i + -1iz3 + 0 + z6 = -2 + 3z3
2i + -1iz3 + z6 = -2 + 3z3

Add '-1z6' to each side of the equation.
2i + -1iz3 + z6 + -1z6 = -2 + 3z3 + -1z6

Combine like terms: z6 + -1z6 = 0
2i + -1iz3 + 0 = -2 + 3z3 + -1z6
2i + -1iz3 = -2 + 3z3 + -1z6

Reorder the terms:
2 + 2i + -1iz3 + -3z3 + z6 = -2 + 3z3 + -1z6 + 2 + -3z3 + z6

Reorder the terms:
2 + 2i + -1iz3 + -3z3 + z6 = -2 + 2 + 3z3 + -3z3 + -1z6 + z6

Combine like terms: -2 + 2 = 0
2 + 2i + -1iz3 + -3z3 + z6 = 0 + 3z3 + -3z3 + -1z6 + z6
2 + 2i + -1iz3 + -3z3 + z6 = 3z3 + -3z3 + -1z6 + z6

Combine like terms: 3z3 + -3z3 = 0
2 + 2i + -1iz3 + -3z3 + z6 = 0 + -1z6 + z6
2 + 2i + -1iz3 + -3z3 + z6 = -1z6 + z6

Combine like terms: -1z6 + z6 = 0
2 + 2i + -1iz3 + -3z3 + z6 = 0

The solution to this equation could not be determined.

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