z^8-(2+i)*z^4+(1+i)=0

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Solution for z^8-(2+i)*z^4+(1+i)=0 equation: 


Simplifying
z8 + -1(2 + i) * z4 + (1 + i) = 0

Reorder the terms for easier multiplication:
z8 + -1z4(2 + i) + (1 + i) = 0
z8 + (2 * -1z4 + i * -1z4) + (1 + i) = 0

Reorder the terms:
z8 + (-1iz4 + -2z4) + (1 + i) = 0
z8 + (-1iz4 + -2z4) + (1 + i) = 0

Remove parenthesis around (1 + i)
z8 + -1iz4 + -2z4 + 1 + i = 0

Reorder the terms:
1 + i + -1iz4 + -2z4 + z8 = 0

Solving
1 + i + -1iz4 + -2z4 + z8 = 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 + i + -1iz4 + -2z4 + -1 + z8 = 0 + -1

Reorder the terms:
1 + -1 + i + -1iz4 + -2z4 + z8 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + i + -1iz4 + -2z4 + z8 = 0 + -1
i + -1iz4 + -2z4 + z8 = 0 + -1

Combine like terms: 0 + -1 = -1
i + -1iz4 + -2z4 + z8 = -1

Add '2z4' to each side of the equation.
i + -1iz4 + -2z4 + 2z4 + z8 = -1 + 2z4

Combine like terms: -2z4 + 2z4 = 0
i + -1iz4 + 0 + z8 = -1 + 2z4
i + -1iz4 + z8 = -1 + 2z4

Add '-1z8' to each side of the equation.
i + -1iz4 + z8 + -1z8 = -1 + 2z4 + -1z8

Combine like terms: z8 + -1z8 = 0
i + -1iz4 + 0 = -1 + 2z4 + -1z8
i + -1iz4 = -1 + 2z4 + -1z8

Reorder the terms:
1 + i + -1iz4 + -2z4 + z8 = -1 + 2z4 + -1z8 + 1 + -2z4 + z8

Reorder the terms:
1 + i + -1iz4 + -2z4 + z8 = -1 + 1 + 2z4 + -2z4 + -1z8 + z8

Combine like terms: -1 + 1 = 0
1 + i + -1iz4 + -2z4 + z8 = 0 + 2z4 + -2z4 + -1z8 + z8
1 + i + -1iz4 + -2z4 + z8 = 2z4 + -2z4 + -1z8 + z8

Combine like terms: 2z4 + -2z4 = 0
1 + i + -1iz4 + -2z4 + z8 = 0 + -1z8 + z8
1 + i + -1iz4 + -2z4 + z8 = -1z8 + z8

Combine like terms: -1z8 + z8 = 0
1 + i + -1iz4 + -2z4 + z8 = 0

The solution to this equation could not be determined.

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